‘Be ready to say the three most difficult phrases in the world: “I was wrong”, “I made a mistake”, and “I’ve changed my mind”.’
Philip Zimbardo, Professor Emeritus at Stanford University.

Someone who will not admit to having made a mistake is not fully admitting it to themselves either. So, they are more likely to keep making that mistake.
  When pressured, they may become accusatory, evasive, or outright lie. When caught out, they lose the trust of others, and the bonds of their relationships weaken a little.
  However, when we are in the habit of admitting to our mistakes we come to realise we can cope with the consequences. So, we become less fearful of another person’s disapproval, and more likely to share our feelings and thoughts.
  And, by accepting our fallibility we come to realise we are not diminished by it. We become less harsh with ourselves, and replace self-blame with self-acceptance.
  So, paradoxically, each time we admit to making a mistake, we feel more comfortable (after the initial embarrassment), and like ourselves more. And, funnily enough, people respect us because we display integrity. That inspires trust. People know we are taking responsibility.
  Further, the more often we admit to being wrong, the more flexible and open-minded we become. We come to trust our judgments, because we know our opinion is not based on protecting our ego, but on seeking the truth.
  None of us like to be wrong, but if we can readily admit to being wrong we have one of the umpteen keys to resilience and core happiness.
  What am I suggesting? From now on, when you are wrong (and only when you are wrong) admit to it clearly and thoroughly. It will be difficult. It will feel like you are committing psychic suicide, but do it. Out loud. Actually say the words, ‘I was wrong. I made a mistake.’
  Then congratulate yourself for transforming a mistake into something positive.

‘No matter how far you have gone down the wrong path, turn back.’
Turkish proverb.

In short, admit to your mistakes. Get into the habit of saying:
‘I was wrong.’
‘I made a mistake.’
‘I have changed my mind.’
‘I don’t know.’

Q. ‘After I have admitted my mistake, what then?’
Look at ways to rectify it, and for ways to prevent it happening again.
   Don’t be harsh with yourself. Being self-critical serves no purpose; it won’t deter yourself from making mistakes in future but it might dent your confidence.
  If you must be critical, criticise your mistake, not yourself.
  If you do catch yourself criticising yourself, retract it.

Q. ‘Does anyone else benefit?’
Sure. When you admit to being wrong the other person can feel heard, or vindicated. Plus, you are setting a splendid example.

Q. ‘When we admit to a mistake we undermine our confidence.’
On the contrary, we come to realise that making mistakes is normal and inevitable, and become less afraid of making mistakes.
 ‘If we are afraid of making mistakes we are less likely to make them.’
  And less likely to be bold. As W. C. Magee once said, ‘Those who seldom make mistakes seldom make anything.’

‘Mistakes are part of the dues one pays for a full life.’
Actress Sophia Loren.

Q. ‘If I admit to my mistakes I might get sued, or sacked, or miss out on a promotion. People in powerful positions don’t admit to their mistakes; that’s why they are in powerful positions.’
This isn’t about building a career, it’s about building person. But consider: when in business you (1) do admit to a mistake you can (2) apologise for it; (3) explain how you will be rectifying the mistake; and (4) explain what you will be doing to ensure it doesn’t happen again. That must be a good thing. To do that in writing is even better. All four steps indicate that you are taking responsibility, and if your boss has any brains at all, they will recognise that and be grateful for it.

‘When you make a mistake, give the people you work with – including those you supervise – a shot at divinity. Admit your error. Own up. Then propose a course to correct the mistake. Never use your authority to mask mistakes. Admit them. Explain them. Apologize for them. Above all else, use them. Allow people to see how you accept responsibility and how you can learn from error. However, do not over-analyse mistakes or indulge in endless rounds of woulda, shoulda, coulda. Once you admit an error, look to the future. What have you learned? How will you keep this from happening again?’
From the book, ‘Patton on Leadership‘, by Alan Axelrod.