it sounds like a pretty typical spat, to be honest.
just as you defend your right to your reaction.......he has the same right. and if he chose to take offense for a bit, isn't that ok?
"Oh so your mad so you are going to ignore me now?"
one response could be - ya know, i am a bit upset right now, but i don't want to take it out on you. i just need a few minutes to sort things out.