Here's something I've often wished I could say: "a true apology begins with 'I'm sorry *I*'," not 'I'm sorry YOU.'." This is a pet peeve of mine.
As in, "I'm sorry *I*... was rude/ hurt your feelings/ was insensitive/ was a jerk/ was thoughtless/ stepped on your toes," etc.
NOT: "I'm sorry YOU ... misunderstood/ took it the wrong way/ are overly sensitive/ can't take a joke/ are such a jerk/ got in my way," etc., etc.
You can not be sorry for another person's actions, only for your own. "I'm sorry YOU" is not an apology. It is a blame game disguised as an apology. It is passive-aggressive. Or worse. The person to whom this fake apology is rendered may THINK s/he heard an apology, but walks away wondering why s/he doesn't FEEL like s/he got one, and instead feels a vague sense of resentment. Should s/he respond, "I forgive you"? Absolutely not! Forgiveness was not sought. One must own one's responsibility for a transgression before reconciliation can take place.
Thank you. I feel better now.