I had a high school science teacher who would say "if you admit you're wrong and change your mind..." and the whole class would respond back "... you aren't wrong anymore!"
And when a kid would assert something incorrect In class, he wouldn't tell them they were wrong, he would help lead them to the right answer and then when they admitted/ accepted the new information, he'd say "now we're both right! Nice work!"
For a bunch of gifted kids whose identity and reputation often was staked on knowing more than most people, it was a great safety valve. No shame in making a mistake, because if you accept it you have learned! Now you are smarter! It always made me feel better.