Im sorry what are they fighting about again??

He's angry that she won't fight with him? He probably thinks she would want to fight if she really loved him, because in a relationship you have to fight, I mean you need to talk about your problems to solve them, avoiding them isn't going to help. So the fact that she won't really communicate how she feels about everything and maybe fight is what bothers him and what bothers her is that he won't do what she wants: which is "avoiding their problems"