I strongly believe that you don’t fully become an adult until saying “I was wrong, I made a mistake” becomes easy. This is the moment when you leave behind the childhood narcissism and enter adulthood.
For children, it’s intolerable to lose face by recognizing that they were wrong. This is why an intelligent adult always gives a child an easy, face-saving way out of a mistake or an instance of bad behavior. Children’s sense of self isn’t yet strong enough to withstand the discomfort of being in the wrong. Trying to force them to apologize or recognize their wrongdoing with words is counterproductive because it delays the creation of a mature sense of self that can easily deal with being fallible.
When I first started working here, I messed up and got a senior colleague into a lot of trouble. This colleague was always sweet to me, and I felt like a bastard. There was no way for the colleague to discover who was at fault. She and everybody else blamed another person who is genuinely annoying and disliked by everybody. It wasn’t easy to go to the senior colleague (who was going to be on my tenure committee) and take responsibility. Looking into her face and seeing her disappointment in me was unpleasant. But I did it because it was the right thing to do. I still cringe inwardly when I remember the moment of having to expose myself not as a competent colleague but as somebody who messes up stupidly. But this is how growth happens.
I see it with students, too. It’s very rare to see somebody who is mature enough not to blame everybody else and their uncle for their own mess-ups. But when I see a rare student who manages to do it, I know that this is somebody who will do fine in life.