veil as a symbol that each man and woman can interpret according to their own consciences.
His act is certainly an honorable one as he is willing to be ostracized by members of the community who become uncomfortable when they cannot read what is on his own face and fear what he may know.

Mr. Hooper wears the black veil because he has come to understand a certain truth about humanity: that we are all sinful, but we attempt to hide our sinfulness from one another by holding up a figurative veil between ourselves and everyone else.  This intangible veil separates us, for as long as we live, from our fellows because we can never truly be known or know another when we attempt to hide this crucial part of what makes us human.

The first sermon Mr. Hooper preaches after he dons the veil helps to make this clearer.  Its subject is "secret sin, and those sad mysteries which we hide from our nearest and dearest, and would fain conceal from our own consciousness, even forgetting that the Omniscient can detect them."  In other words, he speaks of our secret sinfulness and the need we feel to hide that truth about ourselves, even from the people we are closest to.  We would even prefer to forget this truth ourselves, and we can almost convince ourselves that even God is unaware of our secret sins because we are so anxious to conceal them.

When the Reverend Mr. Clark sits by Father Hooper's deathbed, Mr. Clark asks Father Hooper to allow him to remove the veil from Father Hooper's face so that he can meet eternity without it.  Father Hooper, however, is horrified by this idea, and he shrieks, "'Never! [...].  On earth, never!'"  It is clear that Father Hooper wishes never to have the veil removed, and this may be one reason that his parishioners do not remove it.

Further, everyone gathered at Father Hooper's deathbed still seems to fear the mysterious veil.  Mr. Clark even suggests that it signifies some terrible sin Father Hooper had committed.  However, Father Hooper asks, 

"Why do you tremble at me alone? [....] Tremble also at each other!  Have men avoided me, and women shown no pity, and children screamed and fled, only for my black veil?  What, but the mystery which it obscurely typifies, has made this piece of crape so awful?  When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I have lived, and die!  I look around me, and, lo! on every visage a Black Veil!"

It seems to be, in part, this "mystery" that Father Hooper describes that so terrifies the people.  They seem always to have had an obscure idea of what the veil symbolizes -- that each of us has secret sins that we attempt to hide from each other, ourselves, and even God -- but no one wants to admit that they might understand because that would be tantamount to admitting that one has these secret sins on one's soul, and what everyone wants the most is to hide this very fact.  If, in truth, these people really do have even a vague understanding of the veil's meaning, then they would not want to remove it after Father Hooper has died because it is a meaningful and accurate symbol; if, on the other hand, they really don't have a concept of the veil's meaning, then they would not want to remove it because it is such a mystery, and we fear mysteries.

While Mr. Hooper doesn't explicitly state the reason he wears the veil, he certainly gives a number of clues.  He tells Elizabeth, 

"There is an hour to come . . . when all of us shall cast aside our veils . . . Know, then, this veil is a type and a symbol, and I am bound to wear it ever, both in light and darkness, in solitude and before the gaze of multitudes, and as with strangers, so with my familiar friends.  No mortal eye will see it withdrawn."

Mr. Hooper says that there will come a time when everyone will cast their veils aside.  The only time that we all definitively share is death, and so we must cast off our veils in death.  However, only Mr. Hooper wears an actual veil.  Therefore, we must assume that he suggests that we all wear figurative veils, while he claims that his is a symbol: both literal and figurative.  

Elizabeth responds, 

"Beloved and respected as you are, there may be whispers that you hide your face under the consciousness of secret sin."

In other words, there are rumors in the town that Mr. Hooper is wearing the veil out of recognition of some secret sin that he has and is hiding from everyone.  Mr. Hooper smiles at this, his "same sad smile" and says,

" . . . if I cover [my face] for secret sin, what mortal might not do the same?"

Thus, Mr. Hooper seems to acknowledge that his possession of secret sin could be the reason he wears the veil, and he suggests that every single person could likewise wear such a veil because all mortals possess such secret sinfulness.  Suddenly, the veil's meaning seems to dawn on Elizabeth, and she attempts to rush from the room.  Mr. Hooper cries,

"Do not desert me, though this veil must be between us here on earth.  Be mine, and hereafter there shall be no veil over my face, no darkness between our souls!  It is but a mortal veil—it is not for eternity!"

Mr. Hooper admits, then, that the veil will be removed when his soul has gone to God.  He only wears it while the mortal part of him lives, and he promises that it will not remain between them for eternity.  Therefore, we can piece together, as Elizabeth does, that the veil symbolizes the secret sin that each of us maintains, that acts as a veil between ourselves and everyone else while we live.  

The discussion between the Minister and his fiancee Elizabeth is the longest scene in the story and deals more directly with the question of why he is wearing his black veil than any other scene. He implores her not to abandon him, but he tells her that he is sworn to wear the veil for the rest of his life and cannot show his face even to her. He never gives her a candid explanation of what the veil symbolizes or why he is wearing it. He only suggests ambiguous possibilities which show by their phraseology that he either doesn't know why he is doing what he is doing, or else that he is not willing to reveal his secret even to her. For example, he begins two sentences with the word "If" and includes another "if" in one of those sentences:

"If it be a sign of mourning," replied Mr. Hooper, "I perhaps, like most other mortals, have sorrows dark enough to be typified by a black veil."
"If I hide my face for sorrow, there is cause enough . . . and if I cover it for secret sin, what mortal might not do the same?"

Obviously everybody in the story is going to be left guessing, and this suggests that Hawthorne fully intended to leave the reader guessing as well. The question most frequently asked about this story is "Why is the minister wearing that black veil?" But the real definitive reason or reasons will never be known.

At the first service, the parishioners are unnerved by the Minister's veil and most feel a sense of dread, something foreboding. The narrator notes that Mr. Hooper's sermons had always been mildly persuasive; never loud and instructing them with the "thunders of the Word." During this sermon, he is still the same calm orator, but the effect on his listeners (auditors) is different.

. . . there was something, either in the sentiment of the discourse itself, or in the imagination of the auditors, which made it greatly the most powerful effort that they had ever heard from their pastor's lips.

The subject had reference to secret sin, and those sad mysteries which we hide from our nearest and dearest . . .

The listeners are affected by this sermon (because of the subject, the foreboding veil, or both), but their assumptions about the veil have to do with Mr. Hooper. They don't consider that the veil is a symbol of their own secret sins as well. (This is the message Mr. Hooper tries to impart at the end of the story.)

At the funeral, the veil seemed appropriate for this solemn occasion. However, it still leads to mysterious speculation. Upon leaning over the coffin, his veil drooped and he pressed it back to his face. One person thought the corpse shuddered when Mr. Hooper's face was exposed to the corpse. "I had a fancy," replied she, "that the minister and the maiden's spirit were walking hand in hand." One implication is that this person was thinking Mr. Hooper was hiding a secret only he and the maiden (the deceased) knew about, perhaps an affair.

At the wedding, the veil seemed inappropriate. And the guests felt that it brought "nothing but evil to the wedding." The bride was so horrified by the veil that she grew pale enough to cause a whisper that she was the maiden who had died earlier, now returning to be married. At the end of the wedding service, Mr. Hooper catches his own reflection and is also horrified. He rushes off.  

In both cases, the veil causes feelings of dread but also solemnity. These are the effects of the veil. And though Mr. Hooper's veil may indicate his own secret sin, through his veil, he sees a veil on everyone's face, indicating they all have secret sins as well. Ironically, he exposes his secret sins with the veil; they all hide theirs without a symbol such as the veil. In other words, their sins are veiled by not wearing the veil. 

The townspeople definitely do not like the black veil that hangs in front of Hooper's face.  Some think it is a gimmick or a way to protect his eyes from the sun.

Others said there was no mystery at all, but only that the minister’s eyes were weak and needed to be shaded from the light.

But on the whole, the townspeople find it gives the minister a creepy and sinister vibe.  Some of the people even get the feeling that the veil gives the minister some kind of supernatural ability to see each of their hidden sins.  

Every listener, even the most innocent, felt that the preacher had crept up on them and discovered their hidden sins.

The best quote that shows the general feeling about the veil from the congregation comes very early in the story.  Paragraph three specifically.  

“I don’t like it,” muttered an old woman. “He has changed himself into something awful by hiding his face.”

The rest of the townspeople agree with that statement and feel that the mask has somehow turned their beloved minister into something dark.  A great detail left by Hawthorne about the effects of the veil comes a few paragraphs later.  He tells readers that the veil so upset some people during the church service that they had to leave.  That is something that was practically unheard of during that time.  Everybody went to church, and people simply did not walk out during the service. 

At first, the congregation is "wonder-struck" as the Reverend Mr. Hooper greets them on the way to the pulpit inside the church.

In the exposition of "The Minister's Black Veil," the sexton awaits the appearance of the Reverend Hooper so that he can toll the church bell. Soon, he sees the minister appear. It is with "astonishment" that he asks, "But what has good Parson Hooper got upon his face?" Then, as the minister passes others in the congregation, they are amazed at the sight of his face, which is covered by a dark veil.

A rumor of some unaccountable phenomenon had preceded Mr. Hooper into the meetinghouse....He seemed not fully to partake of the prevailing wonder....That mysterious emblem was never once withdrawn. It shook with his measured breath...it threw its obscurity between him and the holy page....Did he seek to hide it from the dread Being whom he was addressing?

Mr. Hooper's veil generates such wonder and mystery that women of delicate natures are forced to leave the meetinghouse lest they faint. Perhaps, too, the "pale-faced" congregation is also a "fearful sight to the minister" as his veil is to them. 

What frightens the congregation is, first of all, the appearance of the minister and their wonder at why Mr. Hooper wears this dark veil over his face. The sexton says that he is unable to believe that Mr. Hooper's face is really behind the black piece of crape. After the parson speaks from the pulpit about "secret sin" and "those sad mysteries" which everyone hides from even their family and friends, the congregation is unnerved and the veil begins to inspire a feeling of dread. Later, they ask if the parson has "gone mad" and why he has transformed himself into "something awful." For, people wonder if Mr. Hooper has done something himself which he wishes to hide, or if he has knowledge of their failings and wishes to hide this awareness.

Nathaniel Hawthorne was known for his stories based in New England and dealing with Puritan religion. His works of literature have become synonymous with sin and righteousness, and the judgments of townspeople.

The Minister's Black Veil is no different. Parson Hooper is the reverend in the town of Milford. He shows up at Mass one morning wearing a black veil that covers his eyes. Immediately the townspeople start gossiping about why he is wearing the veil. Some of the people say that he has gone mad, while others say he is covering a shameful sin. Soon the children of the congregation become afraid of him and the adults continue to gossip about him. Though the townspeople are curious about this, no one has the nerve to ask him why he is wearing the veil. The only person who asks him is his fiancee, Elizabeth. He won't even tell her why he wears the veil. The relationship with his congregation changes dramatically. They now start seeing their own sins that they have been hiding. Most of the people start to have less and less to do with him. Elizabeth, even though she loves him, ends up leaving him, because he won't tell her why he wears the veil and won't take it off for her.

Now that he is alone, he actually begins to become a better clergyman. He begins to gain many converts who feel like they are living beneath a black veil, as well.

"All through life the black veil had hung between him and the world: it had separated him from the cheerful brotherhood and woman's love, and kept him in the saddest of all prisons, his own heart; and still it lay upon his face, as if to deepen the gloom of his dark-some chamber, and shade him from the sunshine of eternity".

This quote sums up how he was now living his life. Elizabeth never married and was with him when he was dying. He tells everyone around him that they all wear black veils. He is trying to show everyone that there is always something hidden within us.

While they are unable to pinpoint their exact reason for uneasiness, Minister Hooper finds himself in a self imposed exile from the company of his fellow man once he assumes the veil.  It seems at first that they are uncomfortable with this new appearance and fear what it is he hides.  If we believe Minister Hooper's dying words, then it is symbolic of secret sin that lies in the hearts of all man; therefore, if they shudder at the sight of the veil it is their own secret sin that they are reminded of and fear the revelation of in their own life. 

Mr. Hooper's parishioners have an intense reaction to his black veil, at first, because it is extremely off-putting.  They are very confused by it because it is so uncommon a thing for a person to cover up their face in this way; we especially like to see the eyes of any person to whom we speak.  They first wonder if it is even their minister behind the veil, and then one old woman says that "'He has changed himself into something awful, only by hiding his face," and another man cries, "'Our parson has gone mad!'"  It is such a strange thing for them to see that they question his motives or even if he has simply lost his mind.

Later, though, especially after he gives his first sermon while wearing the veil, Mr. Hooper's congregation starts to feel very nervous and vulnerable.  The subject of this sermon

had reference to secret sin, and those sad mysteries which we hide from our nearest and dearest, and would fain conceal from our own consciousness [....].  Each member of the congregation [...] felt as if the preacher had crept upon them, behind his awful veil, and discovered their hoarded iniquity of deed or thought.

Mr. Hooper essentially admits that he has "secret sin" himself, sin that he would prefer to hide from everyone, even his loved ones, and he insinuates that his listeners each do too.  They hear him speak and they "quaked" because they felt, suddenly, that he knew that they had secrets too.  For this reason, their behavior toward him changes, and even his fiancee leaves him once she realizes what the veil symbolizes. 

The intentional meaning of the people's reactions to the veil, taken from the perspective of the author, is that they will see in his veil the reflection of their own sins. Also, they will take a good hint that, if the minister had the nerve to call himself a sinner, then they should be doing the same ten times more, and they haven't done so. It is meant to be a message to shock the townspeople. The minister's introspective look at his own life is meant to be a model for others to equally visualize their lives and determine to which level they are living up to the standards of any other church-going folk. The minister is also trying to demonstrate that anyone can sin, and that admitting to weakness and sin is an act of courage, which many may or may not like, but yet is a reality in everyone's life. In not so many words: Nobody is 'holier than thou.'

The members of the congregation of Mr. Hooper are filled with astonishment when they see their minister with a black veil covering the lower part of his face as he steps out his door. But, Mr. Hooper continues on his way deliberately, bending somewhat to look at the ground, yet "nodding kindly" to the members of the congregation who remain on the steps of the meeting-house.

After Mr. Hooper dons the black veil and steps out his door, the sexton who watches because the minister's presence is the signal to ring the church bell, cries out in amazement, "But what has good Parson Hooper got upon his face?" The others are so shocked to see that he has covered all but his eyes with a black veil that when he passes them and nods with gentleness toward them, few return his greeting.

This reaction toward the Reverend Mr. Hooper intensifies the longer that he wears the veil because people wonder if he is trying to hide something or if he sees in their faces some secret sin and, lest he reveal to others this sin, he shields his face. At any rate, they are threatened by the wearing of this veil, and sense a growing discomfiture around him. For this reason, Mr. Hooper is not invited to share Sunday dinners or attend weddings any more.

Therefore, rather than causing his congregation to become open about their human sins, the veil serves only to isolate Mr. Hooper himself. In fact, on his deathbed when he is asked by an attending minister to remove his veil so that others may see his "triumphant aspect" as he goes to "his reward," Mr. Hooper adamantly refuses, 

When the friend shows his inmost heart to his friend, the lover to his best-beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin,—then deem me a monster for the symbol beneath which I have lived and die. I look around me, and, lo! on every visage a black veil!" 

And, so, Mr. Hooper is buried with the veil upon his corpse, having desired to teach a moral lesson by wearing this veil as a symbol of the veil of falseness that each man and woman wears to conceal secret sins.

Before he donned the black veil, the Reverend Mr. Hooper had been known as a pleasant and popular clergyman but not a particularly effective one. His previous preaching was mild and inoffensive but did not make a major impression on his parishioners. In other words, although he was well-liked, he really had not been accomplishing his major task of saving souls.

When he dons the black veil, even though the rest of his appearance is unchanged, he makes a quite different, almost uncanny impression on his parishioners. The parishioners are "wonder-struck" at his transformation and the sexton wonders if it is really Hopper under the veil. The members of his congregation react with fear, awe, and puzzlement to the veil. Even more significantly, they find his sermon more powerful than any he has given before. 

When the Reverend Mr. Hooper first appears with the black veil upon his face, the congregation is "wonder-struck."

Some wonder if he is not really Mr. Hooper, but another minister. Others express their dislike for the veil, saying that it gives them negative feelings. "I can't really feel as if good Mr. Hooper's face was behind that piece of crepe," says the sexton as the minister passes. An older woman mutters that the minister has transformed himself into "something awful, only by hiding his face." Goodman Gray exclaims, "Our parson has gone mad!"

Much like Hester Prynne  of The Scarlet Letter, a novel written by the same author, there is in the Reverend Mr. Hooper, "a sympathetic knowledge of the hidden sin in others' hearts." The variety of these hidden sins are evinced by the various reactions of the members of the congregation throughout the story. Certainly, these Puritans, for which sin is a constant topic of conversation, become uncomfortable and uncertain by the appearance of the veil on Mr. Hooper. For, they begin to wonder what guilt he may be hiding, or, perhaps what he has seen or what he does see in them presently that he wishes not to reveal.

The sexton refers to him as "'good Mr. Hooper,'" and another old woman says that he has "'changed himself into something awful, only by hiding his face'"; both of these descriptions seem to imply that he was liked and respected prior to donning the black veil. People must not have found him "awful" before at all. He had a reputation for being a "good preacher" though he was not particularly "energetic." He is described several times as being "mild" in manner and address, rather than being a more fire-and-brimstone kind of minister. Now, the narrator says,

None, as on former occasions, aspired to the honor of walking by their pastor's side. Old Squire Saunders, doubtless by an accidental lapse of memory, neglected to invite Mr. Hooper to his table, where the good clergyman had been wont to bless the food, almost every Sunday since his settlement.

Therefore, we can ascertain that, before the veil, people wanted to be close to their minister. They wanted to walk with him and to have him over to dinner. They must have felt that he was quite holy and undeniably good. Now, however, they fear his black veil so much that they stop trying to walk with him and forget to ask him to dinner. He was obviously respected and thought of well by his parishioners.

You are right in pointing towards the massive transformation that occurs in Mr. Hooper after he dons his black veil, both in terms of his appearance and what others make of him. However, to consider how he was viewed before he decides to go through this change, you need to look towards the beginning of the story, where the narrator clearly outlines his standing in the community where he ministers:

Mr. Hooper had the reputation of a good preacher, but not an energetic one: He strove to win his people heavenward, by mild persuasive influences, rather than to drive them thither, by the thunders of the Word.

Thus we can see that although Mr. Hooper had a good reputation, he was not famed for the power and vivacity of his preaching, but rather known for his mildness and gentleness. Of course, the black veil changes radically his position in the community and the effectiveness of his job as a minister, as people come to identify their own fallen nature in his black veil.

Reverend Hooper is a complicated figure in the story because we are never quite sure why he doesn't either take off his veil or explain the veil to his congregation.

Hawthorne tells us that Hooper is "a good preacher" who tries to lead his congregation "by mild persuasive influences" rather than through fear and threats of damnation.  Hawthorne is implicitly comparing Hooper to real-life Puritan minister Jonathan Edwards who wrote the famous sermon "Sinners in the Hands of an Angry God," which was the opposite of Hooper's mild persuasion.  When Hooper puts the veil on, however, he essentially becomes a stranger to his congregation because they no longer "recognize" the man behind the veil.

Because Hooper doesn't explain why he is wearing the veil--other than using the theme of "secret sins" in his first sermon with the veil on--the townspeople begin to look upon him with fear.  More important, even Hooper begins to look upon himself with the same fear.  When his fiance, Elizabeth, for example, tries to get him to take the veil off even for a minute, he refuses, but he also tells her she doesn't know afraid he is "to be alone behind my black veil."

Even though Reverend Hooper conducts himself as he always did, he never regains the love and trust of his congregation.  Elizabeth leaves him and doesn't reappear until Hooper is on his deathbed.  The symbolic meaning of the veil--even though his congregation does not know what that meaning is--seems to become more important to Hooper than human relationships, more important, even, than a life with Elizabeth.

One has to question whether Hooper has essentially allowed himself to become a martyr to a symbol, willing to destroy his relationship with the rest of mankind (not to mention Elizabeth's love) in order to send a message that no one quite understands.

The conversation between Mr. Hooper and Elizabeth gives the reader the most information about Mr. Hooper's decision to wear the veil. He explains that he has promised to wear the veil for the rest of his life and will not even show his face to her, his fiancee. However, he never actually explains why he wears the veil; he only hints at a few reasons.

There is an hour to come ... when all of us shall cast aside our veils.

Here, it looks like Mr. Hooper believes that all people wear veils, if only figuratively. The sentence sounds ominous, and the one thing that all people share no matter what is death, so he may believe that in death, people's veils fall away.

Know, then, this veil is a type and a symbol, and I am bound to wear it ever, both in light and darkness, in solitude and before the gaze of multitudes, and as with strangers, so with my familiar friends.

Perhaps Mr. Hooper dons his veil as a symbol of the figurative veils people wear. He goes on to say that "no mortal eye will see it withdrawn," indicating that perhaps he will only allow God to see his face after his death.

Of course, Elizabeth asks about the rumors in the town, all claiming that Mr. Hooper wears his veil because he carries the weight of a hidden sin. He is a bit coy about her question; he says that, yes, he could be wearing the veil because of a secret sin, and if another mortal also carried one, wouldn't they wear the veil as well?

Be mine, and hereafter there shall be no veil over my face, no darkness between our souls! It is but a mortal veil—it is not for eternity!

This is probably the most explicit explanation Mr. Hooper gives for the veil. Here, he admits outright that it is a "mortal veil" and will be removed once he is with God. It could, then, represent the sin humanity carries, one which is removed when someone dies and is forgiven by God.

Regardless of the evidence we can gather, it does seem that Hawthorne wanted his reader to question the reasons for the veil as much as the people in Mr. Hooper's life do.

The author states specifically that the minister's black veil not only hides his face from the world but also gives him a darkened view of everything, including all the people he meets. The following sentence explains not only his subjective perceptions but his objective ones:

On a nearer view it seemed to consist of two folds of crape, which entirely concealed his features, except the mouth and chin, but probably did not intercept his sight, further than to give a darkened aspect to all living and inanimate things.

In other words, the whole world looks dark to him for the rest of his life. This seems to be an unusually morbid choice, since his view of the world and the people in it is probably melancholy enough without the veil. Hooper seems to be suffering from an excessive amount of guilt, and he also seems to be projecting that guilt out upon all the people in his community, especially those of his parish. He naturally makes everyone, including his own fiancee Elizabeth, feel uneasy. No doubt they realize they are not being open and candid with everyone all the time, but this is an impossibility, and no one really expects it.

Reverend Hooper seems to think that everyone in the village, male and female, should adopt his fashion and begin wearing black veils. This would be a weird sort of village, and it would be nearly impossible to get any work done. It wouldn't make anybody more righteous, only more secretive.

Seeing other people through a black veil apparently is effective in making Reverend Hooper think that everyone else is actually wearing a black veil which he or she is not aware of. It is an optical illusion. Furthermore, the effect his appearance has on other people looks to him as their natural state. It makes them reveal their secret guilts and secret fears, even their secret fantasies and secret crimes in their facial expressions and body language, because they believe he can see right through them in spite of the fact that they have been wearing protective masks, or personas, all their adult lives.

Your question points to one of the enduring mysteries ofNathaniel Hawthorne's short story "The Minister's Black Veil"("TMBV").  Reverend Hooper's congregation, so unnerved by his appearance in the veil, fail to place the symbol of the veil in the context of his sermon given moments after he appears in the veil.  The sight of their gentle leader masked by a black veil has turned their world upside down, and their communal response, horrific as it is, precludes even the exercise of common sense:

     'I don't like it,' muttered an old woman, as she hobbled into the meeting-house.  'He has changed himself into something awful, only by hiding his face.'

     'Our parson has gone mad!' cried Goodman Gray, following him across the threshold.

A man whom everyone knew to be a gentle, loving preacher--one who "strove to to win his people heavenward, by mild persuasive influences"--has, by adding a veil to his face, become an object of suspicion and even horror.

Reverend Hooper's sermon, given just minutes after his congregation is seated (but still in fearful awe of the veil), takes as its subject 

. . . secret sin, and those sad mysteries which we hide from our nearest and dearest, and would fain conceal from our own consciousness, even forgetting that the Omniscient can detect them.

Even though each listener seems to feel the effect of Hooper's sermon, perhaps aided by the power of the veil--that Hooper is able to detect each person's "iniquity of thought and deed"--no one appears to connect the sermon's subject (everyone has secret sins) with the symbol or emblem of secret sins, the veil itself.  Even the village's physician remarks on the veil's effect on him, "a sober-minded man like myself," but even he fails to discern the relationship between the veil and the sermon because his intellectual capabilities are no match for the fear inspired by the unknown.

Much has been made of Hooper's failure to discuss the meaning of the veil with his congregation, and there is no doubt that he loses a "teaching moment," but the fact is, he clearly links the symbol of secret sins with his discussion of secret sins.  But the superstitious fears of the congregation veil their own eyes and ears to Reverend Hooper's attempt to teach them that secret sins prevent them from truly knowing each other and understanding their equality in God's eyes.

At the funeral, Mr. Hooper's black veil seems very fitting.  As the narrator says, "It was now an appropriate emblem."  The veil is black, the color associated with mourning.  Its meaning seems connected to the mysteries of life and death, which is also appropriate given that a young woman has just died.  Mr. Hooper seems sorrowful and somber whenever he wears the veil, and these two emotions are both quite proper for the occasion.

At the wedding, however, Mr. Hooper and his veil are much less apt and welcome.  He really alarms the bride, her "cold fingers quiver[ing] in the tremulous hand of the bridegroom [...]."  In fact, she grows so pale that those in attendance say it was almost has though the woman who had been buried that morning had come out of her grave to be married that afternoon.  The guests feel the gloom of the veil as well.  Then, as Mr. Hooper is about to give his toast to the couple, he catches his own reflection in a mirror and panics, frightened even to look at the veil himself, and he drops his wine and rushes from the room.  In short, though the veil "added deeper gloom to the funeral," which seemed appropriate, it "could portend nothing but evil to the wedding."

Good question.  Look at his line late in the story: "Never!" cried the veiled clergyman. "On earth, never!"

From some reason—some deep and mysterious reason—the veil has become an intense symbol for the minister. He's essentially sworn an oath to himself never to remove it, and thus to never stand bare-faced before the world, while he lives. It's taken on a spiritual significance; this is a veil that is also the veil of tears through which all mortal men must see the world. In a sense, he can't; he's admitted he's sinful, and so he must wear this as long as he breathes.

Very interesting question. It is clear that the black veil has both a positive and a negative impact on Mr. Hooper. We are told how the black veil distances him from his own village, and of course, especially his betrothed, Elizabeth, who breaks the engagement. However, it also has the "bonus" if such a term can be used of making him successful as a minister - a "very efficient clergyman", as the text puts it. The text states:

Strangers came long distances to attend service at his church, with the mere idle purpose of gazing at his figure, because it was forbidden them to behold his face. But many were made to quake ere they departed!

So it is clear that the veil makes him a novelty, but one which people are forced to take seriously, for the black veil strikes terror into visitors' hearts as well.

Note too, how the text says:

As the years wore on, shedding their snows above his sable veil, he acquired a name throughout the New England churches, and they called him Father Hooper.

The black veil therefore allows Mr. Hooper to really have an impact as a minister because of his "mysterious emblem", making him a "man of awesome power" and gaining many converts.

Your question correctly poses the conditional "might" as a venue to explain the potential reasons why Hooper makes the odd decision to wear a black veil in front of his face for the rest of his life. 

In reality, this is the one question in the story that never gets answered. The reactions that the veil elicits in the people of the village, however, can somewhat help us to conclude that Hooper purposely wanted to cause specific emotions among the people that reflect what lurks within their hearts. The ultimate reason why he would want this will still remain a mystery that the reader will have to deduce. 

A possible clue to help form a conclusion can be drawn from the minister's answers to his fiancée, Elizabeth, when she demands to know what is going on. Since they are engaged to be married, Elizabeth feels that she has a right to know what could be possibly driving her future husband to make a choice of this nature. However, Hooper's answers are problematic because they are not final. At one point he says to her that, if his veil were a symbol of mourning, 

"I perhaps, like most other mortals, have sorrows dark enough to be typified by a black veil." "If I hide my face for sorrow, there is cause enough . . . and if I cover it for secret sin, what mortal might not do the same?"

If he is not willing to tell the woman that he intends to marry about his rationale, why would he tell anyone else?

Therefore, we can only speculate that the minister wore the veil to cause in the parishioners every possible feeling of uneasiness. Only by understanding exactly what causes their emotions could they be able to learn the inner fears and anxieties that lead them to feel them. This would be a lesson like no other that the minister would be teaching his flock. This also "might" have been the reason behind his decision. The best evidence for this theory is found at the end of the story, when Hooper confronts those visiting his deathbed and the emotions that he conjured in them through the simple fact of wearing a veil. 

"Why do you tremble at me alone? [...] Tremble also at each other! Have men avoided me, and women shown no pity, and children screamed and fled, only for my black veil?"

Here he hits directly on how their inner fears are mirrored by the veil; hence, some equally dark and weird situations must be going on in their hearts. 

"What, but the mystery which it obscurely typifies, has made this piece of crape so awful? [...] When man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I have lived, and die! I look around me, and, lo! on every visage a Black Veil!"

With this, he directly states that he sees a veil in everyone, part of the masking and deception so typical to humans. Why fear the man who dares to expose the lies of the soul? This is a lesson he might have wanted to teach. 

In a society based on the holy pursuit of perfect and election by God, Mr. Hooper dons a veil that provokes a wide range of reactions from his parishioners. The reader never knows the specific reason why he wears this, but we come to understand that he is openly acknowledging some sort of flaw or sin in his life. This gesture puts all those around him on edge.

As he provokes strong reactions to veil, Mr. Hooper also becomes a more effective pastor. Through the "stain" of the veil, he sees sin in all the people around him, regardless of their pretense. This provokes in him a humbling sense of compassion and forgiveness. The first step of forgiveness is acknowledging wrongdoing. Through this, he sees a true brotherhood in those around him.