The key to Dexter (on the TV show, not so much in the novels) is that he has all the usual human emotions and sense of morality. He deals with his childhood trauma and the resulting urges to kill by creating a self-image that he is a "monster." If he just accepts he is evil, then he doesn't need to be troubled or torn by it. A monster doesn't have emotion or morals.
See how that works? It's the way he manages to cope with the impossible contradictions of his mentality. But it just a lie he tells himself in order to survive. So one possible ending for the story is if Dexter starts to finally be honest with himself, but I'm not certain that any person could actually deal with that. How can you continue to murder people, yet be fully in touch with your emotions and moral sense? That's a level of crazy even Dex is incapable of.