How to deal with arguments

Usually when I have an argument with my fiance, I prefer to settle it by maybe agreeing to disagree or just say acknowledge the issue, apologizing and move on. My fiance has a hot temper, instead of seeing each other eye to eye he yells, makes snark remarks and instead of dealing with the issue he just gets passive aggressive, which just leaves things unresolved and angry. He has "learned" to apologize and does it on rare times. He sleeps on it and pretends everything is ok by never talking about the problem. This eats me up because it's unresolved and swept under the carpet. If I bring it up he get moody and says he doesn't want to argue again about the same thing. He's parents fight like this, so he really never learned how to communicate in an argument without him shutting down. I told him that if we want marriage there's going to be issues we have to face together not fighting each other.

I just don't know how to handle his argument style. Any advice on what to do?