Here's a way to short-circuit a particular sort of head-banging argument.

Statements may seem simple, but they actually contain a bunch of presuppositions. One way an argument can go wrong is A says something, B disagrees, A is mistaken about exactly what B is disagreeing with, and neither of them can figure out why the other is so pig-headed about something obvious.

I suggest that if there are several rounds of A and B saying the same things at each other, it's time for at least one of them to pull back and work on pinning down exactly what they're disagreeing about.