Saying “you were right, I was wrong” in front of the group earns more respect than winning ever did.

Conceding in public looks like a loss and works as the opposite. Everybody in the room knows what it costs, and what they take from it is that your account of things can be trusted, since you are evidently willing to update it. Somebody who never concedes is somebody whose agreement means nothing.

Next time you are visibly wrong, say so out loud where it happened rather than privately afterwards. Keep it to one sentence with no excuse attached. Notice how the room treats your next opinion, which will carry more weight precisely because you gave that one up.