“I was wrong” is three words that make you look bigger, not smaller. Almost nobody believes that until they try it.

Admitting error reads as strength because it is expensive, and everyone knows it. Refusing is the cheap move, and people can tell, which is why a defended position always looks smaller than a conceded one. The fear is that it will be used against you; mostly it buys credibility that carries into every later disagreement. None of this is visible from outside until you have tried it.

Say the three words alone, with no explanation attached, the next time they are true. Resist adding context. Then do the different thing, which is the part people are watching for.