Most Helpful Girl
What is keeping you two together? Are you two actually happy in the relationship despite all the fighting? All I'm sensing is a lot of fighting and unhappiness which doesn't seem like a ideal healthy relationship to me. He doesn't seem considerate towards you and the fact that he rather wants to break up then actually work through the problems tells me that he's not even willing to make a effort. I really believe from what you write that this relationship isn't good and meant to be.
With that said, if you truly do want to try to make it work then it will require communication and lots of it. Both of you need to talk face to face about your problems and decide if this will work or not. You can't be broken up but still try to fix a relationship. If you want to fix things you need to work on it together as a unit.