There is no man in the world who does not err, as King David (may he rest in peace) said, “every person deceives”. It is not an embarrassment for a person to admit that he had erred. However, for a person to reinforce his errors and continue doing them is a great embarrassment and shame. Whichever way you look at it, it is shameful, for if he does not realize his mistake, it would appear that he is a fool, and if he does recognize his mistake and is just embarrassed to admit his mistake and therefore would like to continue with the error, then he is increasing the wrongdoing and adding humiliation to his embarrassment, for truth is instantly recognizable, and if he tries to continue in his erring ways with weak excuses etc., anyone who hears about it will laugh at him and realize the evil of his character traits. He, on the other hand, thinks that other people will never realize what he really wants and that he will be able to trick them with his words. It is also the case that the very fact that he thinks that he is cleverer than all other people is itself a very bad characteristic for a person to have.
And who can consider himself greater than our teacher Moshe (may he rest in peace), who admitted his errors and was not too embarrassed to admit them. We find too that the mighty ones of the earth (the Amoraim) used to give speeches in public and say, “the words which I told you previously were a mistake”. Even if he is embarrassed to admit his errors, it is far better to be embarrassed in this world and not to be shamed in the next. For this reason, it behooves a person to have fear of heaven and to admit the truth, in order to honor Hashem, the G-d of truth.