Maya Angelou once said: "When you know better, you do better."
Of course, this takes social consciousness and observation to know any right from wrong programming. Using the Golden Rule puts things in perspective. Meaning: is that how you wish to be treated?
When you realize that you did something "wrong" due to a possible "possessive" emotion or the "devil made me do it" feeling, then that shows you have a conscience. Owing up to that wrong, with an apology, shows you are better then that "emotion" that caused you to be hateful, etc.
By saying, "I don't know what possessed me to say/do that but I apologize," is also like saying, "in your face evil! I'm better than that! Raise yourself up to my level, because I'm not falling down to yours!"
It allows a better state of grace within us ... it frees our soul of negative oppression. Chips on our shoulders suddenly disappear too.
Everyone makes mistakes but don't make it worse by not owing up to it.
Even worse is when you hold a grudge against someone who you feel slighted you and they may not even know they did. Always communicate your feelings ... civilly and respectfully.
In concludion, when someone apologizes, don't be arrogant. Be gracious and just say thanks. Nothing worse then having someone humble themselves with an apology and an argument is started because of a smug retort ... be humble too.
Hmmm ... maybe a couple of cookies, with the apology, might help sweetened the acceptance. I know I'd like it. ;)