I hate being wrong, ask anyone in my family, they will get that slightly weary look and agree (and I am not the only one). I have tried to counter this by learning and improving my knowledge, which helps me, but if I am honest doesn’t help my family. In addition I am a teacher and so, in many situations, could just fall back on authority. Yet in teaching I have realised something important, I actually like it when my students are wrong. I would not say it is the best situation, perhaps, but it is positive. The reason is simple: to be wrong you have to be engaged.
I was thinking about this as I read the post on The Renaissance Mathematicus talking about the birth of HistSci Hulk, sworn enemy of anyone who is wrong about the history of science (a noble and dangerous quest). This might seem to be the opposite position to the one that I gave above. I have felt the sting of his corrections myself, luckily in private not public! It is not opposite, in fact it is the essential counterpart. Being wrong is positive, but only as it helps on the way to better understanding. Reading about how the concepts of gravity were starting to come together before Galileo, and that he did not experiment by dropping things from the tower of Pisa, does take one further. Yet this does not make the original story worthless. It introduces the idea of gravity, the sense there was a change in understanding and Galileo, himself. The correction builds far more happily on this knowledge than it would standing on its own. For this to be effective, of course, we have to accept that stories (especially much loved ones) can be wrong, and more to the point we ourselves might be wrong.
I believe this is actually the great strength of the scientific method, and mathematical proof. Not that they can be used to show things are right, not even that they can show things to be wrong, but that they give a framework to persuade someone they are wrong. They help to develop understanding faster and further.
So do not get embarrassed when you are wrong. Do not get defensive. Learn to embrace it, be grateful, admit it. Then you are learning.
“It is better to open your mouth and learn that you were a fool, than to remain silent and never know.”