I suggest that Frost's "The Road Not Taken" is a bit more lighthearted than the other commentators describe.

In the closing stanza, the speaker isn't creating an anecdote that describes how sorry he is he couldn't take the other road, or how sorry he is that he couldn't take both roads. 

He's creating an anecdote that makes him look unique and special, like a maverick.  The sigh is like a chuckle.  He imagines himself years in the future making up a story or anecdote about how he chose one path over another, because that path was less well-traveled than the other.  That choice, the acecdote suggests, has made all the difference.  But this is an imagining and an anecdote.  He didn't choose the less-traveled path--they are both about the same.  He wasn't a maverick or unique, but his story, sometime in the future, will make him look like one. 

In Robert Frost's "The Road Not Taken," the controlling metaphor of the poem, of course, is that life has many paths which one can take; thus, there is a tension in the poem between the choice that the speaker has made with the one that he has not taken.  In the first lines of the second stanza, the speaker indicates that he is somewhat of an Emersonian, for he "creates a path" for himself on the one that has become "grassy" and "want[ing] wear."

Yet, there is a conservative side to the speaker as well since, he writes, "Oh, I kept the first for another day!"  Here,he does not wish to lose the other opportunity in life, essaying to reserve this other path as he convinces himself that one is as good as the other.  However, his direction is set for him as he traverses the first path, for "way leads on to way."  That is, his destiny is set by the first choice that he has made.  And, it is this fixing of one's destiny that the speaker rues:

I shall be telling this with a sigh

Somewhere ages and ages hence:

Two roads diverged in a wood, and I--

I took the one less traveled by,

And that has made all the difference.

How often one hears a person wonder "what if....?"  What if I had go to a different school?  What if I had gone to a trade school instead of college?  What if I had moved somewhere else?  What if I had not done_____, not married _____etc.  One or two major choices can determine the direction of one's life, indubitably, and "make all the difference," for, as Thomas Wolfe wrote "You can't go home again"--one can not return to what one once was.

As a note:  Be careful when interpreting/explaining a poem that you point to lines that support what you conclude because what you think (opinion) never carries any weight or has any verity unless you can support this judgment with lines, passages, etc. from the text. 

In this poem, in my opinion, Frost is trying to tell us that we are able to convince ourselves of things that are not true.  He is also trying to show that people want to be unique and important.

If you look in the poem, every time that the speaker thinks that one road is different, he realizes that the other is really just the same.  Yet he ends up saying that he will look back and "know" that the road he took was different.  This shows my first point.

For my second -- why does the speaker want to convince himself of this?  I think it is because we want to be special -- we all want to think we are taking the road less traveled.