Apologizing is powerful because it forces you to take responsibility for your own actions. When you blame others for how you feel and act, you are giving away far too much power to someone else. I want to be in control of my own emotions, actions and reactions. No one else should be blamed for those. I always have a choice when it comes to how I behave, and where my words or attitudes are hurtful to others, I must apologize, in order to set myself free from guilt and blame.
I don't understand why saying, "I'm sorry" is so hard for some people. It's as though it costs them some kind of high price to admit any wrong and apologize for it. I look at it the opposite way: not apologizing is a price too high for my own soul, because it means I'm dodging responsibility for my own actions, and lying to myself.
We all make mistakes, lots of them, on a daily if not hourly basis. Coming to terms with this provides a freedom so immense, it feels like the horizon on the prairies. It opens up your spirit to breathe deeply and heal from any expectations placed on yourself to be perfect. Accepting that mistakes are okay is as liberated as you can get in this lifetime.
Excuses are the opposite of apologies. Making excuses for bad behaviour doesn't do anything for you, or for the relationship that has been damaged. Apologies heal the rift and free you up from the guilt you feel, and hopefully prevent you from making the same mistake again. Facing up to the truth of how our actions affect others, and not backing away when we have hurt someone, is the path to personal and relational redemption.
Having just come through a difficult conflict, I realized again how powerful it is to say, "I'm sorry." If you don't mean it, there is no point in saying it, but when you mean it, the power that lives in those two words can transform any situation. True humility and repentance blazes the way to a stronger and healthier relationship, but the best benefit of all is the freedom it offers to the person who apologizes. The other party wasn't willing to take responsibility for their actions, but I still liberated myself from the painful situation, because focusing on what I can control is the only way to escape with my dignity intact.