My mom taught me how to apologize for everything, even how to notice that I play a role in what happens, so even when it isn't my fault entirely, obviously I must have done something or there wouldn't be a problem between us. I've tried to get away from this tendency by telling people that I am not responsible for their feelings, as I have always felt responsible, but truthfully, we are not in control of another's feelings or reactions. Still, I say I am sorry when someone is hurting, I find the empathy or sympathy by replaying the situation until I discover how I upset them according to their point of view. According to mine, I may still not be at fault, but that's not as important. It's not about who's right, it's about who needs the apology.
Also, my dad is almost always at fault in my mom's perception, so I have watched him apologize for things that he had no control over, I have watched him say he was sorry just because she was angry and he didn't know how else to calm her down. I could have learned by his behavior, apologies make things better, no matter who is responsible.
I usually won't apologize until I feel it. I make myself feel it or I give up and try to move on without forcing the issue, such as I'll say I'm sorry that they were hurt by my actions, but I won't apologize for the actions themselves. If they don't catch me side-stepping, everything turns out ok.
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Let us comfort each other, and move tenderly when we are able. Let us hold hands and walk bravely, or fearfully together; for as long as there is Love, there is Hope, that everything will be okay, including the things we say are not.