I personally have more faith in someone that says ‘oops, did that wrong, but not gonna happen again’ than I do someone that gets their back up, blusters and outright lies.
I do think the caveat here is, as a leader, it’s to take responsibility for your mistakes, not ‘admit’ to them by shoving the blame onto others. Admitting mistakes by tossing others under the bus is just as bad, if not worse, than not fessing up to them at all.
I have a ‘leader’ that doesn’t make mistakes, and if mistakes are made they’re not her fault. Someone else did something wrong and mislead her because she doesn’t make mistakes…..Basically the expectation is that we will work to cover her mistakes, cover her butt all the while knowing that if anyone calls her on the mistakes they’re our fault anyway because it’s our fault we didn’t cover for her…..I’m sure you can imagine just how fantastically we respect this person and their ‘leadership’.