Personally, and not trying to answer for OP here, but I think it's always unhelpful if someone makes it about the person, not their behaviour, eg 'he experiences bulimia' is much better than 'he's a bulimic' cos then it's showing that the person just has that behaviour, it's not actually who they are.

Also, and again personally, cutter is a very difficult word to use, especially when you are one. I think maybe it's how my friend who is gay calls himself a poof but would be offended if someone else referred to him that way. It can be a sign if strength if you are that person, but a derogatory term from someone who doesn't understand.