Forgiveness is when the person is ????? (appeases) you. Chazal don’t speak of ‘asking Mechila’, but rather of appeasement. That means when the person recognizes the wrong that was done, takes the blame, and explains how he is not of the earlier mindset and that it won’t be repeated.
When this happens, and it is not ??? ???? anymore, you are supposed to forgive. Forgiveness in this case means the acceptance of the fact that this person changed.
In our selfish generation, forgiveness had to be rebranded as self serving. Like all good things, you obviously gain from it, but that’s not quite what we are after here.