One of the things I hated most as a child was being bullied to apologize. It wasn’t the apology itself that hurt, but the humiliation of being forced to apologize. Usually, the thing being apologized for was manufactured by my siblings; the alleged wrongdoing was done by me in self-defense. Almost always, when a “real” apology was needed, I would have apologized on my own.

It is a good rule in life never to apologize. The right sort of people do not want apologies, and the wrong sort take a mean advantage of them.
Quotation from P.G. Wodehouse, The Man Upstairs

The best apology against false accusers is silence and sufferance, and honest deeds set against dishonest words.
Quotation from John Milton