Why does Holden characterize himself as a liar?
In my opinion, he does it because he is unwilling to confront any of the truths in the world around him that make him uncomfortable and so by placing himself in the category of something false, he is also not forced to accept any kind of truth about himself either.
He isn't willing to really accept the fact that his brother Allie is dead. He isn't really willing to deal with the fact that his parents aren't close to him and that he doesn't feel any connection to his schoolmates, etc. Everyone around him is phony.
But he is also a phony in his mind, he lies all the time, he cannot be trusted. This way no one expects him to tell the truth and he can deny anything he says, so if he actually tells something true and someone calls him on it, he can deny it and just say he was lying then too.