Any idiom or phrase for "refusing to admit one's mistake or one's own lack of knowledge, abilities or achievements"?

Question

Is there any idiom or phrase for this?

refusing to admit one's mistake or one's own lack of knowledge, abilities or achievements

For example, You ask your friend a simple question, but he doesn't have a clue. When you tell him the answer, he says, "Of course I knew. I'd just forgotten!" (He doesn't want to admit that he didn't know the answer at all!)

Or, another example:

You play tennis with your uncle, and he gets creamed! But he says, "Of course I could win if I were younger!" (He doesn't want to admit that his tennis isn't good enough!)

Answer 1

This is called face-saving.

intended to prevent someone from feeling embarrassed or having to admit that they are wrong

a face-saving compromise/exercise/deal

The European Commission agreed a face-saving compromise to defuse a bitter dispute with Germany over subsidies.

[Cambridge]

Answer 2

If that person really means what they are saying, that may be said to have a big ego.

Someone with a big ego has high belief in their abilities and skills. This belief is sometimes just a perception which does not necessarily mirror the truth.

This would not apply though if the person does not really mean it, and just says it for the sake of proving something to other people.

Answer 3

How about self-justification? From M-W:

self-justification: the act or an instance of making excuses for oneself

Examples of self-justification:

I knew that. I just forgot.

I would have won easily if I were younger.

I would have won. I just lost interest.