to forgive is to forget

I heard it in the lyrics of the song of our neighbors. It says "to forgive is to forget".

I must say that this should be true. When we have a fight with someone, if we forgive them, we should forget what happened and move on. But I see a lot of people saying they have forgiven but they will never forget what person did to them.

Honestly, in my case, I usually forgive someone because I have forgotten what he/she has done. Give me a few hours and I can't even tell the story anymore as I have forgotten it. Of course, it is not complete forgetting. But my anger is gone.

I think it is necessary that once we say we forgive someone genuinely, we must forget what happened. Because keeping it in our mind will only bring the pain back and make us mad. Also, when another argument arises, we may bring that issue back and make deeper wounds in that person's heart and our own heart.

How about you guys? What's your view with this matter.