I am sorry to hear.
I was in a relationship like that as well. My ex and I both cut and both fought CONSTANTLY. It didn't help our cutting and we'd both be telling each other to stop. I finally realized that it just wasn't right for either one of us. We broke up (for good) after two years of being together.
I am the type of person that doesn't believe there is "one" right person for everyone. I believe there are many. See, during our stages in life we change dramatically. At certain stages, we should be with this person. Then at a different stage, we should be with this person. So essentially I believe that we are with people for a reason at certain times. There was a reason I was with my ex, there's a reason you're with your boyfriend. However, it doesn't mean that this is the right person for you. He shouldn't be telling you that you're going to break up and then tell you what to do. He obviously can't control what you do.
I hope that you don't turn to SI, but I know that when you're in that period of your life as I was it seems to be the only thing TO turn to, so I am not going to try to sit here and tell you not to like he is I am just going to say to try to turn to something else if you can. Plus, try to work it out. Try to stop fighting, but it takes two to tango and he needs to know that. I had to learn after a long time that my ex wasn't the one for me, and it COULD turn out that way for you as well.
Hope it works out for you and I've helped some.