I’d start by describing the two classic bad apologies: 1) “I’m sorry you feel hurt by what I’ve done.” (This is an attempt at an emotional salve, but it’s obvious you don’t want to put any medicine in the wound.) 2) “I apologize for what I did, but you also need to apologize to me for what you’ve done.” (That’s not giving an apology. That’s asking for one.) Proper apologies have three parts: 1) What I did was wrong. 2) I feel badly that I hurt you. 3) How do I make this better?