In "On the Knocking at the Gate in Macbeth," why is De Quincey so puzzled at the scene of comic relief? What is his basic argument in the essay?
First, I offer a slight correction to your question: Thomas De Quincey's essay was not about the Porter scene. Rather he concerned himself only with the knocking at the gate.
From the earliest times of his familiarity with Shakespeare's Macbeth, Thomas De Quincey was bothered by one thing in particular: as soon as the Macbeths succeed in murdering King Duncan, they hear a knocking at the castle gate. What perplexed De Quincey is why he had the peculiar feeling of sympathy or at least an interest in the reactions of Macbeth to the sound.
...the knocking at the gate, which succeeds to the murder of Duncan, produced to my feelings an effect for which I never could account. The effect was, that it reflected back upon the murderer a peculiar awfulness and a depth of solemnity...
De Quincey had felt for years that, although his thoughts should have been with the dead King, instead they were with Macbeth's horrified reaction. He comes to understand that this was Shakespeare's intent all along:
Hence it is, that when the deed is done, when the work of darkness is perfect, then the world of darkness passes away like a pageantry in the clouds: the knocking at the gate is heard; and it makes known audibly that the reaction has commenced; the human has made its reflux upon the fiendish; the pulses of life are beginning to beat again; and the re-establishment of the goings-on of the world in which we live, first makes us profoundly sensible of the awful parenthesis that had suspended them.
I, myself, see other things in the knocking on the gate, one of which I will mention here. Where De Quincey uses the word "sympathy" in a dispassionate sense, more like attention than sympathy, I have always felt real sympathy for Macbeth. My sympathy does not extend to Lady Macbeth, because she does not act with the kind of remorse with which her husband reacts.
Remember, just hours before, Macbeth had pleaded with Lady Macbeth to spare the life of the king, to forget the whole thing. He had given himself and his wife many reasons why the killing would be a very bad idea. She, of course, convinces him otherwise. The knocking on the gate reminds us of Macbeth's sympathy for the king and of his own weakness. Finally, as if he could undo it all, he desperately cries to the unseen knocker at the gate:
To know my deed, ’twere best not know myself. Knock knock knock
Wake Duncan with thy knocking! I would thou couldst!
In De Quincey's "On the Knocking at the Gate in Macbeth," De Quincey is puzzled as to why this comic relief "...reflected back upon the murder a peculiar awfulness and a depth of solemnity;..." He knows the scene produces this effect, but for years he couldn't figure out why.
The remainder of the essay tells the "why." In short, De Quincey explains that normally sympathy lies with the victim of a murder. But Shakespeare needed to "throw the interest" on to the murderer, instead. Shakespeare needed to arouse a "sympathy of comprehension" for Macbeth. A murderer such as Shakespeare would create must possess:
...some great storm of passion--jealousy, ambition, vengeance, hatred--which will create a hell within him, and into this hell we are to look.
De Quincey then reasons that when a murderer such as this kills, the normal human world vanishes, and a fiendish world replaces it. This happens when Macbeth kills Duncan.
Furthermore, all "action in any direction is best expounded, measured, and made apprehensible by reaction."
Therefore, the knocking that opens the comical scene both wakes up, if you will, the dormant normal human world that vanished when Macbeth killed Duncan, and begins the reaction to the murderer and the murder.
Again, the world that vanished during the murder reappears with the knocking, and this ignites the reaction to the murder. This is why the comical scene produces the effect it produces, according to De Quincey.
Thomas de Quincey argues that an audience must feel a "sympathy of comprehension" for Macbeth and Lady Macbeth in order for the play to be effective. He does not intend nor expect the audience to applaud them for their murderous actions but rather to try to understand the feelings of the characters. The knocking at the gate is a call to the audience to come back to reality, back from the depths of evil in Macbeth's hellish world. The knocking has a jarring effect on the audience, summoning them back into the everyday world, so they can become keenly aware of the gravity and horror of the actions of Macbeth and his wife.