Personally I think saying only "i'm sorry" when you have offended a person is insufficient. I have taught my daughters that if they are truly sorry for what they have done they will say "So-and-so I am sorry for (name the offence) I was wrong, would you please forgive me?" Sometimes they won't forgive right away and that is their option, but God does tell us if we will not forgive, then He won't forgive us, so they are up against God now and not the person who asked for forgivness. But from my own experience it is hard to say "I forgive you", if I am still angry and I will actually tell one of them "you know I don't want to talk about this right now" or "just leave me alone right now". Neither are sufficient, but God doens't let me off the hook and before long I must reconcile with them or things are not right.
So to answer your question, they might not say I forgive you at the moment, because they really don't want to.