TL&DR – the thing any leader worth their salt must absolutely do – without exception – if they wish to secure respect and generate good will is this: Admit they are wrong when they are wrong.
A great leader isn’t great by being infallible. No human being is, nor ever will they be while retaining said humanity. Making mistakes is not only inevitable, but it is also the only way we learn.
Every true leader has reached their standing through weathering the test of time. The main difference between a leader and a follower is that a leader has failed more times than a follower has even tried … but with a twist. A leader fails fast and fails cheap… and always learns from his failures/mistakes.
Now, knowing that mistakes/failures are normal, any sensible person with a brain knows that you do make mistakes. You are not a machine. Not only that, they will unavoidably catch you making them. And when they do … admit your wrong doing. Nothing bad with that.
Actually, successful leaders encourage their people to point out mistakes so that they can be corrected.
Mind you, for best results, this needs to be done in a nurturing and constructive fashion. No one likes a “know it all” nor a “rub it in your face” attitude.
You will know when you have perfected this craft when you catch yourself being able to admit you’re wrong in a nonchalant manner, like it’s “business as usual”. Just keep in mind two complimentary and very necessary things for constructive results.
Don’t make the same mistake twice… or at least not in a short time frame.
Focus on the learning element in the experience.