There's a lot more to forgiveness than forgetting; the main thing is love. Still, it's wrong -- and spiritually unsafe -- to leave people with the impression that they can hold tight to the memory of wrong and call it forgiveness.
Does God really stop remembering our sins? Actually, yes, he does. It's not a problem with his omniscience, it's a deliberate decision to wash us clean. It's a decision not to recall a memory:
For I will forgive their iniquities,
And remember their sins no more. (Jeremiah 31:34)
Claiming that God must remember is not truly standing up for God's glory. When he stands up for his own name, he proclaims that he will not remember:
It is I, I who -- for My own sake --
Wipe your transgressions away
And remember your sins no more. (Isaiah 43:25)
Then what if we remember a sin of someone we have forgiven? We forgive again; we forget again. If the forgiveness is still firmly decided, then putting the memory out of mind will be easy.
Human memories are not like God's. They are like an old radio signal -- they fade with time and distance. If you do not boost the signal it will be lost, the further away you go. That's why we repeat things we want to remember, or look at them time after time to refresh our memories. Most memories fade with time. The memory of old wrongs could easily be forgotten, if only we would let them.
Our minds are like a sieve. We forget where we left our keys. We forget where we left our watch, or our phone. We forget what we had to eat just a day or two ago. Our minds have a natural tendency to forget. It takes a serious effort on our part to be able to recall all the wrong that someone did us awhile back. Don't we remember because we pay attention to those things, and keep close track of them?
If God -- God the omniscient, God the all-knowing, God the Almighty -- can manage to put away a memory and remember it no more, then how much more should we forgetful little creatures be able to put away a memory and remember it no more.
I have often -- too often -- watched my own mind call up old sins. A person who wronged me will cross my path again. And the old memories will rush into my thoughts. It takes effort to put these things out of mind. I admit that I resort to some silly tricks to chase out the memories. When there are images that I want to remove from my mind, sometimes I picture those images as printed on paper, and then imagine a paper shredder, and shred them. Sometimes when memory brings up images, I picture the memories falling into a video game, and I picture myself using the video controllers to blast the memories out of existence. Sometimes the memories are sounds and words; I picture them as a recording, and I picture myself hitting the "next track" button.
Are these amateurish ways to handle memories of someone's sin? Yes. But I'd rather have these silly tricks in my mind than the bad memories. Ideally, I should be able to replace these memories with other memories of the person being kind or friendly or trustworthy or helpful. One day I hope I can remember things that build love and compassion just as easily as I remember wrongs. Because we really are fighting an uphill battle against our memories of sin, until we learn to love the other person. Forgiveness hasn't reached its goal until there is reconciliation.