It occurs to me that some people see apologies as a weakness. They think apologizing is an admission of failure. You win and I lose or I win and you lose, depending on who's apologizing. Win/lose thinking. As much as I hate to admit it, I've sometimes let that point of view dictate my behavior to the extent that I didn't apologize when I should have or continued to hold a grudge against someone who did.
But when I'm vital, I recognize that truly apologizing is an act of empathy. It's saying, "Yes, I can respect where you're coming from; I've even been there myself! It makes sense to me that what I/you did/said sucked and I hate that that happened. I've learned another little something about getting along with people from this exchange. Thanks."
Then I change my behavior accordingly and hopefully it sticks and makes life more pleasant for me and everyone around me.