Simply trying to forget the wrongs that are done against us is like spray-painting a rusty old car. It seems like an easy solution at first, but eventually the rust breaks through and the problem is worse than before.
Well-meaning Christians often support the "forgive and forget" model of forgiveness by appealing to God's forgiveness, as in Jeremiah 31:34. In their view, this text means that forgetting precedes forgiving. They say that if we don't forget, we can't forgive.
There is a sense, of course, in which God "forgets" our sins. Once He has forgiven us, He will never use them as evidence against us. But the all-knowing Creator can't forget things in the way that we do. Data can be erased from a computer's magnetic memory, human recollections can be obliterated by time and disability, but all of history is constantly before His gaze. From eternity to eternity, God is the same. The divine Author of Scripture caused the sins of Jacob, Moses, David, Peter, and Paul to be recorded for our benefit. He hasn't forgotten their sins in a historical sense, but they will never be used as grounds for condemnation. It is our sin's debt -- the rightful wages of our sin -- that God "forgets."
God doesn't expect us to wipe the sins of others from our memory. In fact, we probably won't be able to, no matter how hard we try. He certainly wouldn't want us to pretend that we have forgotten things we can't forget. What He desires is that we forgive sins committed against us (Matthew 6:14-15) the way He forgives our much greater sins against Him (Matthew 18:23-35).
It takes greater forgiveness to forgive a grievance that we remember clearly than to forgive a grievance that we have partially forgotten. Merely ignoring our memory of a grievance isn't forgiveness; it's only suppression of anger. Genuine forgiveness, like God's forgiveness, clearly sees the offense and then forgives it by withdrawing the penalty and continuing the relationship. It's natural to deal with our anger by suppressing our memory of an offense, but it's supernatural to remember it clearly and renounce our right to revenge. Revenge must be left in the hands of the only One who is always objective and just (Romans 12:19-21).