I only apologise if I do something that I didn't intend to do; for genuine mistakes.
I don't pretend to be a nice person all the time. I'm amicable, and I try to be friendly and as considerate as possible, but there are going to be times when I disagree with other people and we have an altercation. I don't see why I should apologise for a stance I take, or something I said or did in the heat of the moment - why should I regret it? I never ask people to apologise for such things, nor do I expect them to unprompted. All people are different; if I don't like something someone said to me, or something they did, it's not for me to demand or expect an apology from them. I deal with it and move on; it's in the past, and it's not worth dwelling on...and if it IS, then it's going to take a hell of a lot more than just "I'm sorry" to erase it, isn't it?
If other people can't do the same, I'm not responsible for that, and I'm not going to apologise to them because they can't come to terms with the fact that I am different to them, and that I have different attitudes and values. I see it as incredibly insincere to apologise for words spoken in haste - which are often words of truth as one sees it in my opinion, as they have little time to think about their responses and so say what they are feeling at any given time - or for actions deliberately plotted at the time and later regretted. I refuse to do it. I'm sorry, but that's just the way I am.
As a clarification, it's not difficult for me to admit that I'm wrong because of this. But there is a huge difference between an admission like that and an apology, at least to me.