It helps to understand HOW people respond when they fight and family background plays a big part in that. In my house, I'm more like Lin, the emotions tend to hit like a freight train and explode. My husband is much more passive aggressive (which I never understood until recently) and neither of us did well at reading each other, especially during a disagreement. When the fight starts, I'm usually the one yelling and screaming and overcome with anger and hurt, so by the time my husband hits the point of screaming, I instantly go completely calm (mostly because he is hit the point of absolute irrationality).
Studying up on different types of communications and learning about "non-violent" communications helped us a great deal in being able to deal with the other. This is something you can do together. He is used to people fighting "his way" and equally doesn't fully understand how you don't respond the way he is used to. It's likely that he can see it as a sign that you don't care as much or such, because you don't have that sudden flash of emotion. Keep talking about it, but in small doses. Also don't make him feel that only he has to change to match what you want. Neither way is inherently WRONG and there is always things each of you can do to fight better.