With some people, being right costs more than it pays. Pick your peace and let them keep the trophy.

Winning an argument and improving your life are different outcomes. With certain people, proving your point costs you the evening, the week and a good deal of your own calm, while changing nothing about what they believe. The trophy is available and it is not worth the entry fee. Letting someone stay wrong is sometimes the more self-respecting move.

Before the next round, ask what you actually want out of the conversation. If the honest answer is to be acknowledged, and you already know that is not coming, step back early. Save the energy for arguments that change something.