The Irony of Self-Harm
After Nicholas' suicide attempt, he takes a step back and examines his habits. He notices that, while he thought he had been writing poetry as a creative outlet, he had been pushing himself to work so hard that it was actually a form of self-harm. He had hid behind the guise of creativity and construction in order to emotionally cut himself, so what he thought was self-protection was actually self-harm. This is the trick about self-harm; it often looks like any other normal activity, but the motivation or actual application of the activity is hurting the individual doing it.
The Irony of Intellectual Companionship
Much of Nicholas' angst and dissatisfaction in life is his lack of perceived intellectual companionship. He's desperate to talk with someone who can understand him and meet him where he's at. Ironically, when Conchis serves this purpose in Nicholas' life, Nicholas finds himself still dissatisfied. He's missing the service that Alison offered him -- love. While Conchis can analyze and muse and lecture and all that, he doesn't love Nicholas. And both elements are necessary in a person's life. Once again, intellectual companionship -- as the object of all of Nicholas' desires -- wasn't the final solution.
The Irony of Depression
Depression is a tricky and far-reaching illness, which manifests in different people in various ways at different times. In Nicholas' case, his existential boredom and creative frustration can aptly be described as depression. He's intelligent which causes him an unusual amount of pain and dysphoria because he can see a lot of true things -- unpleasant truths -- about the world around him. The irony here is that Nicholas feeds his depression like some people do their egos. Attached to it for comfort and familiarity's sake, he nurses the illness with lethargy, negative thought patterns, complaints, etc. Although he doesn't need to "be fixed" or "cured" or whatever from depression, Nicholas doesn't need the illness in order to be intelligent. He makes an error in his estimation of what makes him valuable as a person. This is a fairly common, though ironic, reaction to depression.
The Irony of Alison's Breakup
Alison and Nicholas love each other, and they're a solid couple. They relate to each other and maintain their differences. Unfortunately neither one can communicate how much they care about the other person, so they remain silent and interpret their partner's silence as unhappiness. This poor communication is the reason they break up. Although they both adore this relationship, they don't tell the other person and they do make assumptions about the other person and ultimately this costs them their happiness together.
The Irony of Conchis' Mentorship
In Conchis Nicholas believes he's found a true friend at last. He has yet to meet anyone so intelligent and tasteful and similar to himself in every way. Ironically, Conchis is none of these things, except when he mirrors Nicholas. He's playing a long con on the boy, so he shows Nicholas exactly what he believes he wants to see. None of it is real or born out of genuine concern for Nicholas, despite how perfect their relationship appears to Nicholas at the time.