I always tell people that I easily forgive and forget. Forgiveness is the simple part, but forgetting is the complex part.
You know, out of the many things I have learned from humanity, is that some of us can be very manipulative and smart and cunning, quick to twist words to soothe them.
I always try to be careful with people who are repeat offenders and at the same time regular players of the forgive and forget card. I see them as high-level psychopathic manipulators, lol. The description might seem extreme, but I am serious. Every time they say “forgive and forget,” my brain automatically translates it to “forgive and don't learn."
I think having the idea that forgiving and forgetting have to go together is not healthy in any way. How does someone even forget something just like that? I know people pass through trauma and experience some kind of self-induced amnesia, but even a therapist would tell you how unhealthy and even dangerous it is. And for this reason, people find it hard to forgive because that's obviously what happens when you think you can't forgive without doing something—forgetting—which is impossible.
The place I know the saying came from is the Bible. I don't know if there is any other source, though. I think it was a verse where God said he would forgive the iniquity of men and wouldn't remember the sin of men. And the Bible is a book I understand you can't just read like a textbook, and should be read and understood personally, to avoid things like the confusion around the forgive-and-forget thing. That verse simply means God wouldn't punish or hold a grudge against men for their forgiven sins.
When someone hurts you, you can't just forgive and wipe the memories away just like that; it's mostly impossible. As a human being, the highest you can do is forgive and be without grudges, and maybe over time, you forget. But you haven't forgotten, it doesn't mean you can't get rid of the pain.
For example, I borrowed some money and the person promised to return it at a specific time because I would need it urgently then. And when it's time for payback, the person fails to pay back, deliberately or not. If the person comes again to borrow more, I can decide to take the risk or not. And if it repeats itself, I will learn my lesson. If the person comes again, I would turn the person away without thinking twice. No grudge, no pain, the offense has been forgiven but that doesn't mean in the name of forgiving and forgetting I would be a fool and repeat the same thing.
To forgive is indeed an incredible feeling. If you truly forgive and let go of the burden of carrying a grudge, even a vivid memory can't take away the freedom and relief, nothing would make you dwell on the deed, and you would move on with your life. So let's forget about the “forget" in the saying and focus more on the "forgive."