Why does Humbert Humbert incriminate himself?

The great mystery of the novel is why he does that. However, a fairly brief answer would be that he is mad. He references his own madness several times throughout the novel, and we ourselves can see his insanity through his desire to kill Quilty and success in doing so. It also allows Nabokov to treat his audience as the "jury" and have us be bedazzled by Humbert's language - ask yourself if you condemned him or exonerated him at the end.