tl;dr Should I forgive the people who did me wrong?

I believe forgiveness is just closure for the person who did you wrong, and it helps bolster the their own self-belief that they are not bad people. I have had people do me dirty in the past, and some have been orbiting looking for forgiveness or a chance to normalize relations, but I have swatted their attempts usually causing them to become more aggressive and angrier. Only amplifying their past behavior. To the point they would rather bad mouth me to total strangers, to keep me from enlightening people about their past behaviors.

I guess my question is, in your experience are there any major drawbacks to not forgiving people and allowing your relations to stay "cold".

This question is in-regard to women and BB/white knight orbiters.

Thank you.

Edit 1: And past "friends".