Most arguments are two people talking at each other.
You obviously think you are right. You begin arguing, but then something terrible happens: they make a strong point that you can immediately tell is correct, proving you wrong. Now here is your dilemma. Conceding would be the right thing to do, but it would open the door for your opponent to gloat and be a “sore winner.” That’s too much for your ego, so you dig in, knowing full well you are defending a wrong position. I want to suggest a way out of this...
Before you argue, both of you need to say and acknowledge
“If I end up changing my mind and conceding that you’re right, will you promise not to gloat?”
This should help you both drop your guard and actually listen. Once gloating is off the table, changing your mind is safe to reveal. And then the search for actual truth can happen.
And if someone refuses to say it, they likely came to win, not to get to the truth.
So reconsider whether to argue with them at all.
Bonus points
“What specific evidence would it take for each of us to change our minds?”
Saying you’re open-minded is easy. Naming exactly what would change your mind makes it real. Again, if they refuse to answer, you’ve learned what you needed to know.