Cut to the chase: Forgiveness is for your benefit, not the S.O.B.
Now why is that?
Granted, if you have done something to someone that you later wish you hadn't, and the someone tells you not to worry, it's done with, etc., you (in the role of the S.O.B.) do feel better. The act of their forgiveness removes your feeling of guilt. This equation requires that you (in the role of S.O.B to the other person) recognize that you acted in a way contrary to your true self and you wish to make amends, undo the damage, etc., fix it! The other person may or may not bestow 'forgiveness' but the sheer willingness to make amends results in relief for you. Okay, got that. Now to the main point.
"To err is human, to forgive divine." Thus said poet Alexander Pope. There are many ways to interpret this truism, all correct. And, like a parable, reveal different levels of understanding. Pope implies that forgiveness - releasing obligations from another - is close to the nature of the Divine. Errors - thoughts and behaviors that result in harm or negativity - are human, that is, separate from the Divine. (The capitalized Divine is a placeholder for whatever description you have of First Cause, Source Energy, God, Creator...)
Many people have difficulty with forgiveness. They believe that to "forgive" someone is to "let the scoundrel get away with it!" Thus leading to conditional forgiveness - when you do this/that, then I'll let your off the hook! That's a recipe for continued misery, until the person becomes so miserable (a.k.a. hit the bottom) that he or she literally gives up (trying to make the other person behave or change) and thus finally allows a change in thinking.
That's why forgiveness brings relief - it changes the focus of your attention away from the S.O.B. and whatever that was about, to something else. The more you think about, give attention to, lie awake at night reviewing mental scripts, and such about the offending situation and S.O.B, the more similar feelings you'll attract. The Law of Attraction never ceases and is always in play with unerring neutrality. Whatever you think about you attract/experience more of the same. That's just the way it works. Like gravity, you can work with it or not. It's still there, doing its thing.
It seems that the fear that the S.O.B. will "get away with it" is the issue. Somehow, we think that we must feel anger towards the S.O.B. and curse him or her for their dastardly actions. Does the S.O.B. care? Does the S.O.B. give a rat's ass that you're angry or upset with him/her? No. And that can make you even more angry! Angry feelings produce more angry situations. Now, if you truly enjoy feeling angry and devoting your mental energy to another, then you're certainly free to do that. Law of Attraction will assist you.
I think that most people would rather feel good than feel bad. I mean, why do anything unless the result, or expected result, is a good feeling? Therefore, when holding a resentment or angry feeling towards someone, there is some kind of expectation that there will be a "good" feeling as a result. "Yes, George," you say. "I'll feel great when that son-of-a-bitch gets what's coming to him!" How long will that take? Do you have the power to give the get? How are you feeling in the mean time? Remember, this is about YOU, not the S.O.B.!
The Law of Attraction insures that the S.O.B. will experience what he/she gives attention too. You don't have to worry about that. In fact, you don't have to worry at all. If you do, it's because you want to. And if you want to, then you're enthralled by the S.O.B. and not acting in your interest. (You know that many S.O.B.'s love owning your attention! Makes them feel powerful.)
In a sense, you mortgage your happiness to whatever the S.O.B. does. That's an arrangement that doesn't favor you! Every day your target your resentment, anger, etc., the more equity in the mortgage. Oh, by the way, the equity goes to the S.O.B. Forgiveness is your way out of this bad deal.
Forgiveness is to THINK ABOUT SOMETHING ELSE. You cannot become free of someone if you keep them in mind. "I forgive you, you miserable piece of humanity." Those are words, not intentions. You do not have to, and really can't, think about the injury, injustice, etc., in the desire to forgive. If you forgive, you forgive. Which means that you give yourself permission to think and give attention to something you feel good about (or certainly feel better about.) Do that for a bit and it becomes easier. Keep it up and you won't even notice that you no longer dwell on the rascal or miscreant. You're living your life, for your health and wellbeing now.
And, you can always use the magic word.