You can stay and argue, or you can get back to your mission. (This includes imaginary arguments).
You have more important things to do. It’s usually better to go do something productive than it is to try changing someone’s mind.
Once you enter into an argument, you’re entering into another person’s world. And that world may not be a rational one. You’ll probably just end up frustrated.
Most of the time, when we enter into an argument, we’re lowering our standards. We’re lowering the bar of what’s important and we’re lowering the bar of how to communicate properly.
Set the bar high. Force people to come up to your level. Not in a pretentious way, but in a way that says “we can do better”.