Hello- I'm new at this so please bear with me.
This is more than a communication problem.
Have you tried to talk to him when you weren't in the middle of a fight? Have you said to him that you'd like to figure out a way to disagree without getting upset? If so then how does he react?
The key to any good relationship is knowing how to disagree.
In general, if this is the way someone deals with conflict in a relationship (running out, cold shoulder, upset), then this person will not success in any long term relaitonship.
Battlingtobalance, on the surface, I would agree that this isn't a communication issue.