But that's the thing, he may be a rebel, but without a cause. The kind of guy who always complains about the world but does nothing to change it, and when he sees someone trying, he even makes fun of them. The game is supposed to be satyrical, so I think that he really doesn't have an answer, he's supposed to be this kind of guy, and when he realises that even though he suggested that the idea of "fighting demons to save the world" was stupid, it was much more meaningful than anything that he ever did and probably ever would do. He has his own motives, his personal vendetta against demons, but it's not really focused, he doesn't have a plan or anything, he's just angry.
It's worth pointing out that this is supposed to be also a spiritual journey for Dante, you would see him evolve as a peson throughout the game. He starts as just this punk guy who hates demons and doesn't give a crap about the world, and later on he's willing to risk everything to save this girl he didn't really care about at first.