I wouldn't advise you to break up with him, I'm not sure what good that could do. I think it's something you should deal with together. A break-up for the sake of 'saving' another person is just going to put you in a hell of a state, and leave him hurt and bemused.
I do understand where you're coming from though. My boyfriend's sick to death of me suggesting he leaves me lol. I freak out a lot. Incredibly he just calms me down, says 'you're pushing me away again, and I'm not going anywhere'. You guy sounds like a decent one too. If you explain it to him he'll feel more involved and realise the 'pushing away' is probably a symptom of something else other than an unhappy relationship.
I can't say why you push him away, but the eating disorder is probably at the heart of it. For me, I feel I've got a lot on my plate whereas my boyfriend is settling into his new life (year abroad) much better than he ever has before. It's hard asking for help when you know the other person is ok - you start thinking 'well their only problem at the moment is me'. I felt bad for being down and tell myself that no-one would want to put up with me. For me, pushing someone away until they give up fulfills that idea, regardless of the fact it's me doing the pushing, and they'd happily hang around. Sadly, when you're in a state like that, sometimes being 'right' and being on your own and feeling sorry for yourself becomes more important than admitting you need help, and more importantly that the problem isn't in the relationship.
Like I said, sit down and talk it through with him. Write it out first so it makes sense in your head, and he'll hopefuly get it a bit better. You don't have to go through it alone and as long as he feels involved and up to date, I'm sure the 'pushing away' won't be an issue.
I'm sure in the rational moments you know you want to be together right?