First let me say that the phrase "forgive and forget" cannot be found within Scripture. We are commanded in various scriptures such as; Matthew 6:14, Ephesians 4:32, and Colossians 3:13 “to forgive one another”. Scripture teaches that a Christian who does not practice forgiveness will reap bitterness according to Hebrews 12:14-15 and loss of eternal rewards according to 2 John 1:8.
Forgiveness is a decision of the will and since God commands us to forgive, we must therefore make a conscious choice to forgive. Forgiveness brings freedom to the offended not the offender. The offender may not desire forgiveness and may not change; see Matthew 5:44. Ideally, the offender will seek reconciliation, but if not, the one wronged should still make known his decision to forgive.
Furthermore, scripture does not command us to forget sin nor does it say that God forgets our sin. Scripture teaches removal in Psalm 103:12; “as far as the east is from the west, so far does he remove our transgressions from us” and in Micah 7:19; “He will again have compassion on us; he will tread our iniquities underfoot. You will cast all our sins into the depths of the sea.” Scripture further teaches in Isaiah 43:25, Jeremiah 31:34, and in Hebrews 8:12 that our Lord “remembers our sin no more”. These cited and well known passages do not teach that our Lord forgets our sins. However, it clearly teaches that; “He no longer remembers”. This is not double speak or semantics. Let me explain. Our Lord is omniscient meaning that He is all knowing. If our Lord forgets then He ceases to be all knowing. It’s like asking; “Can God make a rock so big that He cannot move it?” He can’t because He would then cease to be omnipotent.
So what does scripture mean when it says that “he remembers our sin no more”? It means that he no longer holds it against us. He doesn’t forget it He treats it as though it never happened.
Therefore, we are commanded to forgive sin and act as if that sin had never occurred. We remember the sin, but live as if we do not remember it. This is how one fulfills Paul’s teaching in Ephesians 4:32.