The comic structure of Emma comes from her repeated misjudgments, called in advance (or at the moment) by Knightley and the increasing gap between Emma's perception of herself as a better judge than Knightley and the evidence. We are told, for instance, that "it was most convenient to Emma not to make a direct reply" (40); that "Emma made no answer, and tried to look cheerfully unconcerned, but was really feeling uncomfortable and wanting him very much to be gone" (42); that "Emma remained in a state of vexation" (42); and that "he had frightened her a little about Mr. Elton" (41). In other words, Emma's conscience indicts her even where her rhetorical skills force a draw. Or rather, her refusal to admit contradiction ("there can be no use in canvassing it" ) leaves him with the alternatives of laying bare her contradictions--she is "far from allowing" (38) that she wrote Harriet's answer but then admits but then admits she influenced Harriet "a little" (41)--or accepting her good intentions ("there was very little for me or for anybody to do" (41).
Of course this is what is called in logic as a false dilemma or an A/B fallacy. It is quite possible that Emma could have good intentions (though the previous chapter makes us doubt that her primary concern was for Harriet's well being and not her own loneliness) and nevertheless be wrong as to the application of them. The question of good intentions is a good fall back for the weaker debater, though, because it is extremely hard to falsify. Knightley can (and does) say that Emma has been no friend to Harriet Smith, meaning that her actions will not promote Harriet's well being. Emma's definition of friendship is that of a state of feeling. [Ironically, at Box Hill, Knightley will insist that he is serving the office of a friend in hurting Emma, suggesting that it is at times when we are most insecure of our motives that we insist on their purity, rather than our own success, being the mark of our authenticity.]
This argument goes on for a bit, and there is a weird sort of cold war quality to it, as there is to many of Emma's and Knightley's interactions. By that I mean that through most of the book, conflicts between people are rarely played out between them directly. The lives of others, and their interaction with these others, becomes the ideological battleground on which central arguments are played out. In some cases secrets and power discrepancies prevent direct confrontations from taking place (such as with Jane Fairfax and Frank Churchill), but at others, such as the ball where Elton snubs Harriet (to hurt Emma) and Knightley dances with Harriet (to please Emma), Harriet serves as Highbury's own little Vietnam.
This may sound too harsh towards Knightley. The standard approach to this passage is that Emma's immaturity fails to bow before his superior logical and insight. It is worth noting, though, that Knightley confirms that Harriet's leaving Highbury would be a loss to Emma (39), but one that Emma would gladly give up. Emma responds, "I cannot help wondering at your knowing so little of Emma as to say any such thing" (39). The retreat to the third person here is odd, and it is perhaps telling that this is the first poitn that Emma picks up in contention. To be sure, Emma's explanation is that she disagrees with Knightley's contention that this is "a good match" but this statement is doubly, unconsciously ironic given Knightley's claim that "you would not regret your friend's leaving Highbury" (39).
It is also customary in discussing this chapter to contrast Knightley's budding egalitarianism (evidenced by Knightley's praise of Robert Martin's "sense") with Emma's residual class prejudice (in claiming that the Martin's are beneath her and even her friend). The question of class prejudice is a tricky one in Emma. It is clear that the Martins act in marked contrast to the Eltons, especially, and that they often act the part of the gentry even while the gentry are acting crassly, materialistically, shallowly, and superficially. On the other hand, Emma and Knightley never question the appropriateness of their own place at the top of the social pecking order. To be sure, they accept the burdens of noblesse oblige more graciously than the Eltons, and are always free with a carriage for Miss Bates or some meat for a poor local family. For all Martin's independence, Knightley seems to like him most for his deference to him. That Martin opens his life to him--that he can still interact with a pleasant acquaintance despite of class differences while Emma cannot--may play a material part in Knightley's estimation of Martin's conduct and willingness to live with prospective changes.
This chapter also provides examples of Emma's budding psychosis.
Okay, that's a strong word, but consider this assertion from Emma about Harriet's claims in society:
As to the circumstances of her birth, though in a legal sense she may be called Nobody, it will not hold in a common sense. She is not to pay for the offence of others, by being held below the level of those with whom she is brought up--There can scarcely be a doubt that her father is a gentleman--and a gentleman of fortune.--Her allowance is very liberal; nothing has ever been grudged for her improvement or comfort.--That she is a gentleman's daughter, is indubitable to me; that she associates with gentlemen's daughters, no one, I apprehend, will deny.--She is superior to Robert Martin. (39)
What is Emma's evidence that Robert Martin is inferior to Harriet? It is clear to Emma. Her allowance is liberal. She associates with gentelmen's daughters. Well, the latter is actually a bit of a stretch in its use of the plural. Harriet associates with one gentleman's daughter--Emma. Harriet is superior to Robert Martin because Emma declares her to be so, and Emma believes she can bend social rules to her will, that by acting as though a thing is so, she will make it so.
Then again, Knightley asserts, "Robert Martin has no great loss--if he can but think so" (42). The irony of this juxtaposition is that in a patriarchal society, assertion is often sufficient for those of power or privilege to carry the day, and Emma is only really trying to act in reference to Harriet as men in her circle act all the time. Her father can declare a light snowfall a blizzard and his word is sufficient to make it so. Frank Churchill can declare a haircut sufficient reason to go to London and nobody (excepting another man) will contradict him. Elton can declare Emma's amateur painting worthy of a frame and a place of honor, and thus it is. It may be that Emma's delusion is not so much that she thinks she is particular but that she thinks she is not, not so much that she thinks that as an individual she can do what others cannot (bend reality to her will) but that as a woman she thinks she can do what others can (make pronouncements that others have to live with).