The given quote that a good man tries to fix his mistakes and that having too much pride is bad is very true. If one cant concede he made a mistake, he isnt being honest with himself.
There are many examples of this throughout literature. One great example is the story of Oedipus Rex. In the play written by Sophocles, Oedipus is a king who unknowingly killed his father and married his mother. At the beginning of the story, he refused to believe a blind prophet who told Oedipus that he had married his mother and killed his father. He was too filled with pride thinking he was very great and lucky to be king. In fact, he was so sure that what the prophet had said was untrue that he vowed to find and punish whoever killed King Leios (the former king and Oedipuss father).
As the story continued, Oedipus began to realize that he actually did kill his father and marry his mother. He remembered that a drunk man told him he would do that, which was why he left the city-state he grew up in. He also realized that his wife/mother Jocaste and father Leios had disposed of a son who was prophesized to do what Oedipus did.
Once Oedipus realized the situation, instead of being too conceited and ignoring the truth, he accepted it and punished himself, the killer, as he said he would. This shows that while at some times Oedipus was very arrogant and conceited, when he realized he had made a big mistake he was a good man and paid his dues.
One can learn from the story of Oedipus that if one makes a mistake he should try to remedy the situation, not ignore it and hope the problem goes away. Being a good person means admitting when one is wrong and showing remorse for a mistake.