Ennui is a sickness, and the Doctor has a bad case of it. For very nearly a thousand years he’s been running around doing everything he can to save the universe from itself only to finally come to the inescapable conclusion that the universe simply doesn’t care. If that’s the case, then why should he?
Well, he shouldn’t, and doesn’t; he’s well out of the Saving the Universe business. Why can’t everyone go away and let him mope in peace? He’s had enough, and if people want to accuse him of apathy, so be it.