Forgiveness is an internal thing. You can forgive an enemy and never talk to them again for each other's sake. The difference is that you are no longer haunted by their existence. You can move on with your life.
It's like I'll always encourage forgiving cheaters so that you can move on with your life. That doesn't mean taking them back. I wouldn't encourage taking them back. But move on so that you can find someone better who doesn't cheat and live happily with them instead of dwelling on that cheater and letting them and their actions haunt you for the rest of your life.
This is beneficial from a purely selfish perspective. To forgive is to make inner peace. It doesn't require any religious motivation whatsoever.
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