Admitting you were wrong while your friends watch costs a little pride. It buys a lot of credibility.

Getting something wrong in private costs almost nothing. Getting it wrong in front of people who will remember feels like losing standing. What actually happens is stranger than that: people trust somebody who concedes, because it means their agreement is worth something too. The small amount of pride you spend buys a reputation for being straight, which pays out for years.

Concede one thing out loud this week, clearly, without the softening phrases. You were wrong, they were right, and that is the whole sentence. Then watch how nobody treats you worse for it.