I apologize if I realize something I did unwillingly or without thinking first caused someone I care about pain or sorrow. I know I’m not a perfect human being, and if apologizing will keep someone from hating me for something I did which I truly regret, why shouldn’t I? Hopefully it will keep me from making the same mistake again.
An apology is, in my mind, not all about saying “I’m sorry I did what I did” but a way of saying “I will try to improve myself as a person and not repeat this mistake”, and it’s up to the other person if they will give me a chance to do so and thus forgive me, or not.
I do think many people apologize too much though, for any little thing. It takes the meaning out of the act of apologizing, and some people’s “sorry’s” are just basically meaningless to me.
I’ve thought about this recently since getting a kid, because kids think they can do any shit they want and then say “I’m sorry” and all is forgiven. And sadly, a lot of adults have that mentality as well.