Why did Tyler Durden shoot himself?
Tyler is created by "Jack" (Ed Norton / Narrator) as half of his personality. The half that would live fast, die young, and basically be everything that Jack was not.
So, by "killing" Tyler, Jack is saying that he chooses to end the Tyler portion of his personality, and return to his real life as Jack.
You could either take this literally, as in he actually put a gun in his mouth and fired a shot. Or, since most of the world around him was a fabrication once his insomnia took hold anyway, you could say that Jack just made the choice to get rid of Tyler, and the whole gun-in-the-mouth thing was just a physical representation of his mental choice.
In either case, if you look closely you'll see that the bullet came through his cheek/jaw, which is a survivable wound. But, maybe this just adds another layer of complication to the plot, it might not matter.
Sorry to be confusing, if I was. In a nutshell, Tyler never existed and the "shot" was Jack's way of getting rid of his other personality.
But either way, he was really concerned about project Mayhem and then suddenly he shoots himself. Good job, you killed your alter ego. They still blew up the buildings. gg
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