He shouldn’t apologise if he didn’t actually change his opinion – but then you can also not make the argument that he made a mistake. Mistake sort of implies that he acknowledges he made a mistake – which he doesn’t.
You can’t forgive someone if they aren’t asking for forgiveness.
Forgiveness is really about being open hearted and keeping no record of wrongs. On the cross Jesus said:
"Forgive them for they do not know what they are doing"
Jesus had the perfect right to be angry, but he wasn't. He forgave while people were mocking him and killing him. Stephen to first martyr said the same thing while he was being stoned to death.
You can’t forgive someone if they aren’t asking for forgiveness.