Leave the other person a way to back down without looking dumb. People fight hardest when they feel cornered.
LEADERSHIP
LEADERSHIP
Cornered people stop defending the point and start defending themselves. Once someone can only agree by being publicly humiliated, they will keep arguing long after they know you are right, because conceding now costs more than being wrong. That is arithmetic rather than stubbornness. You built the trap when you closed the exit.
Leave them a line they can take: say the information was easy to miss, or that you only saw it yourself last week. Skip the summary of how long you have been right. Winning quietly is the version that actually changes something.
Who did you corner when you could have left an exit?
Free, with nothing to buy inside it.