Misidentified characters
Multiple times in the novel, people are confused about who the other characters are. Horace falls in love with Agnès and accidentally confesses it to the very last person he should—Arnolphe himself. When Horace gets a chance to figure it out from Agnès herself, she just calls him by another name, so still, he never quite figures out which guy is the bad guy after all. Then Arnolphe realizes that Enrique is Agnès's father, but at first, he thinks his daughter is some other person and he thinks his schemes are going to actually work. Then he realizes his faux pas.
The irony of Arnolphe
First of all, Arnolphe has the ironic quality for fearing the very thing he wants most, a woman's attention. Then, he becomes more ironic by acting in such an obviously villainous manner to get a virgin with a perfectly pure mind. He obviously doesn't know much about people.
The irony of the title
There's a sense in which the intention of the play is misstated by the title, The School for Wives, because one assumes the title means the convent being a school for Arnolphe's wife, but actually Arnolphe is the school for Horace's wife. Arnolphe is left humiliated and alone, unmarried.
The silly hero
One lovely aspect of this story is that Horace never realizes how much danger he's in, because he's completely unfazed by Arnolphe's foolish and ineffective plans. Actually, Horace isn't really the brightest kid in the whole world, but he still manages to do as a young guy what Arnolphe couldn't do in his whole life—have fun with a girl. That's all it takes for this young hero to succeed, that he views his crush as a person and a friend, instead of as an object, and for that alone, he's a hero. He's a silly guy, but he's a good one.
The judging father
Well, if there's one thing that Arnolphe wasn't expecting, it was that all his efforts were for nothing. Just at the crucial moment, there is a Deus Ex Machina, a divine judge who enters the story for salvation of the victim and for judgment against Arnolphe. It's ironic that such a man was Agnès's father all along. It's more ironic that Arnolphe never figures that out in the many years he knew Agnès. He'd never even met her father—that's how far away from real courtship he is.
