Yes, yes, and no.
To be fair, most of the things I say or write in anger I don't regret. If someone is using his or her financial, familial, or health status as a pity shield, I will call him or her on it, no matter how rude it may be. If someone is making hurtful remarks in the guise of "jokes," I'm going to confront them. Conversely, if someone has a stick up his or her rear and takes something too seriously, I'll tell that person to get a life. Most of all if someone lies or makes false promises directly to me, I show no mercy. I don't regret the fallout. I may only regret that it didn't happen sooner.
However, when I do see where I'm in the wrong, I will apologize. The key there is the offended party had better explain how I'm wrong. If a person is offended and proclaims I'm a meanie or dismisses me by saying I'm "stupid," that person isn't getting an apology from me. But if that person actually shows me why he or she feels that way or explains where the error in my thinking is, I'm very likely to offer a complete apology.
The problem is without fail, the people to whom I apologize say they accept my apology, but then continue to hold past wrongs against me. If someone genuinely apologizes to me, I forgive them on the spot and wipe out much of the memory of whatever grudge we have. Life is too short to be angry with people over anything, no matter how heinous, once an admission of guilt is provided, and the twins of contrition and repentance are shown.
But that same attitude is never applied to me. Instead of forgiving and forgetting, whatever was done seems to be a scarlet letter attached to me. It does get annoying after a while.
I offer peace and I get war in return. One day I'll be at the point where I can consistently forgive people without even an apology, but I'm not there yet. And so the cold war simmers.