My husband is the one that is usually disengaging, over what seems to me to be nothing. It feels almost like he's trying to train me to always agree with him or something, by walking away when I say something he doesn't like.
He's also admitted in the past to liking being angry because he likes 'the rush of it'. So he needs his anger fix.
They may feel challenged or belittled if you try to point out "well maybe..." or other things when they personally feel so strongly or right in one way about something or a situation. Like you aren't taking "their side" when really, you're just trying to give a different view and have a general/normal conversation naturally.