I've said before that most conflict comes from acting on assumptions, and its hard to rescind those assumptions and apologize afterwards. But, as I think Kleinbro has said, apologies have a lot of power. I like all of the points you make, lil, and I try to incorporate them when I need to say sorry. But I feel like a lot of the time, people can't apologize using this method (i.e. genuinely) because of how difficult it is for most people to apologize, and the fact that these sorts of apologies require an amount of self-reflection that is difficult a lot of the time. I think the biggest step to get past that initial hurdle is to make the conflict less about "winning and losing" and more about solving an issue together. Us vs. the problem, I guess.