He fancies himself a Nietzschean ubermensch, but is confronted with someone who is his moral superior; someone who can do things he can never do, and be something he can never be, in ways that he cannot equal. The fact that he can't deal with this is a double humiliation he can never bring himself to face. Not just that he has a superior, but the fact that he cannot overcome himself, the fact that he lets himself be ruled by spite, proves he isn't the man he likes to think he is. Because admitting this to himself is unthinkable, he is driven to his insane quest on a raft of flimsy rationalizations in order to avoid facing his own flaws.
Put more simply, you know how fat women on tumblr think it's societies fault that they're not considered attractive? That's fundamentally the same psychology as Lex Luthor.