You won’t win anyone over by proving they’re dumb. Give them a way to change their mind and keep their dignity.

Being shown you were wrong in front of people costs more than being wrong did, so most of us defend the position rather than accept the embarrassment. That is not stubbornness; it is a reasonable trade. If you want the outcome instead of the win, you have to build an exit: a reason it was sensible to think that, a new piece of information, a way to agree that does not look like surrender.

Hand somebody a dignified route out this week instead of a scoreboard. Say what was fair about their reasoning before you add what changed. Let them arrive at it in their own words.