In Psalm 25:7, we pray with David, "Remember no more the sins of my youth; remember me according to your mercy, because of your goodness, LORD."

If God forgets something, it's not just forgotten. It ceases to exist. More, it never did exist. That is the degree to which God, in His freely bestowed mercy, forgives us, and restores our relationship with Him.

Human forgetfulness doesn't work that way. If you forget some wrong I've done, that doesn't mean I didn't do it. The effects of my act remain. It may well be the case that those effects are negligible, in which case we can speak of human forgetting in the same metaphorical sense of Divine forgetting, to signify the full restoration of a relationship. But there are also cases where the effects aren't negligible and the full restoration of the relationship is not within our power.

Our responsibility as Christians is to do what lies within our grace-aided power, but not what lies beyond.