Saying sorry is a good way to catch your ego doing its thing. The harder it is to say sorry, the easier it is to see your ego. Your ego is all that pain trying not to say sorry.
Children have a difficult time telling each other that they are sorry when they have done something on purpose. If they are angry, the last thing that they want to do is admit that they were wrong and try to make another person feel better. They become fully absorbed in their egos and have no empathy for the pain they have caused. If they are forced to apologize, they may say sorry in a way that inflicts additional pain.
Adults have similar struggles. Saying sorry can be an act of compassion. Saying sorry can be an act of humility. If your ego isn’t all caught up in being humble and compassionate, saying sorry can challenge your ego. It becomes difficult to say. That is why it is a good practice to say sorry. It becomes extra good practice if you force yourself to say sorry and the other person tells you you should be. You can notice your ego as plain as the full moon when that happens.