I'll tell you an interesting personal story. My father was a stubborn man. He never admitted when he was wrong, he always defended his position even when it was hopeless.

One day he was disagreeing with my little brother and my little brother just said "I was wrong. I lost my head."  And my father laughed. He and my little brother laughed a long time.

Ever after that day, my father had no problem backing away from something he said that later he realized was wrong.  He would just say "I lost my head" and start laughing. It's funny how sometimes children teach parents.