...and you can't rationalize with the irrational. Of all the things I have learned in my decade of Education, those are two absolute truths. You can spend a lot of time spinning your wheels trying to get someone to see your way of thinking, but until they step away from their own perspective, its all for naught. Sometimes all you need is to press the pause button. My advice is to stop trying to get your point across, and just stop. Once ego and anger dissipate, productive dialogue can happen.
But sometimes it can't. Not everyone wants to resolve conflict; some people use conflict as their lovey. What else would they snuggle up with at night, rub across their fingers, turn over and over in the minds? These people, the conflict-lovers, see the actions of others through fun-house mirrors. They don't see what we see, and so our help does no good. Our prayers do.