All (or nearly all) in the movie Fight Club can be explained by the protagonist's mental disorder. But why does he stay alive and get rid of his alter ego after shooting himself? What is the meaning of this?
When you watch the scene closely (I wish I had screenshots...might have to dig later) you can clearly see that he doesn't shoot himself in the back of the head, but really in the side of the mouth, albeit farther back than his cheek.
Even if you feel around with your tongue you can feel that it is just skin and muscle and nothing important until you get to your jawbone, we can assume he hit just before that, which explains why he is still alive. A shot like that would hurt a tremendous amount, and probably bleed a lot, but it won't kill you outright, not unless you don't find proper treatment or something to close the wound. Note I AM NOT A DOCTOR
The rest of this answer is C&P of my answer to a related question