I've noticed I'm inclined to do this. Sometimes it's profitable to stand your ground, but when you go around and around in circles saying very little with someone, but still saying it, you're trying to have the last word with little effect.

Recognise the pattern, and break out of it when it's in your interests to do so. Letting them know you're washing your hands of it is an option, but it's the washing your hands of it that matters.

This happens especially on the Internet, so learning to leave it, let it go, is a good skill to have.