I have thought many times why is it so difficult to admit that we were wrong. What makes it that hard to say "I'm sorry, I was wrong". Is it that important to always be right? Or is it just about not admitting that we were wrong?
"In fact, until we have to admit to someone that we were wrong, we aren't wrong, are we? I mean, that's all that matters, what the others think of us, right?"
This is what our self-preservation instinct tells us. "Keep calm, you're right, somebody else must have screwed up". But you have to be better than that. You have to realise that you cannot always blame someone else. You have to realise that in every problem there was more than one person involved.
The only thing stopping you from learning is admitting to yourself that you were part of the string of factors that led to the problem. Step over that phase and then you can ask the next question, "What can I do better next time?". And that's how you improve.
It's difficult to admit to yourself that you did wrong. It means stepping down from that high pedestal you have put yourself on.
But don't worry, it's the first step to rise even higher and higher.