25 “I, even I, am he who blots out your transgressions, for my own sake, and remembers your sins no more. — Isaiah 43:25 NLT
God forgives us of our sins and chooses not to remember them or hold them against us. No where in the Bible are we instructed to “forgive and forget”. Like many sayings attributed to the Bible, this one is not in there. While it is a beautiful expression and idea, I am not sure that humans are capable of forgetting those transgressions, either the ones we have committed against God or those that have been committed against us. While we may not be capable of forgetting, we are charged over and over with the responsibility of forgiving. That we can do, because it is an act of the will, it is a decision that we make. God has certainly told us that His forgiveness of our sins requires us to forgive others
Be kind and compassionate to one another, forgiving each other, just as in Christ God forgave you. — Eph. 4:32
There are many other verses emphasizing the fact that we must forgive. These verses also show us how our relationship with the Father is affected by a lack of forgiveness. (Matt. 6:15) They also show us how a lack of forgiveness causes us to become bitter (Hebrews 12) and how unforgiveness will cause us to lose our reward (2 John).
The “forgetting” part means that we should be so sure and certain about our decision to forigve that the transgression no longer affects our relationship with the person committing the act. It is no longer a part of any discussion we have or any decision that we make. It means that just as God has justified our standing with Him, we do the same for the transgressor. It is as if we had “forgotten” or as if that incident had never happened.
Notice in the passage from Isaiah that God said He would forgive them for His sake which indicates there are some good things that come to those who do the forgiving as well as to those who are forgiven. So, if for no other reason, we need to forgive for our own sake.