I used to treat being wrong as a private emergency. Correct it, hide the evidence, move on before anyone noticed the shape of the mistake.
The first time I said “I was wrong about that” in a room of people I respected, nothing collapsed. Someone else said they had been carrying the same error. The meeting got shorter. The work got better.
The lesson is not “be humble.” It is more mechanical than that: the cost of defending a small inaccuracy is almost always higher than the cost of naming it. Pride is expensive. Revision is cheap.