I know he needs help, but I can't help someone who doesn't want to help themself.

That line from your post really says it. That sounds like a really horrible choice to make, but please don't feel guilty if you decide to kick him out. I'm assuming that you offered him a place to live while he is recovering, not a place to stay while he is drinking himself to death. You can always tell him that he is welcome back when he is ready to quit drinking.

Good luck with whatever you do.