What Makes God Forget Our Sins?

One answer to that question is faith, our own and also that of those who love us. It was the faith of the four friends of the paralytic that prompted Our Lord to tell this man that his sins were forgiven and because they were forgiven, those sins were forgotten. Yes, a physical healing may have taken place, but it was the healing balm of Christ's mercy that allowed the man to walk away in the sight of the doubting and disbelieving crowd. Many in that crowd may have doubted who Jesus was, but at the sight of the once paralyzed man, some may have turned to God in awe and praise.
In my own life, I know first hand the paralyzing effect of sin. The shame, guilt, and fear that comes with those sins further the paralysis. Like the man in today's Gospel, I too had a friend whose faith was stronger than my own at the time. At a time when my sins and their effects held me in a paralyzing grip, my friend brought me to Jesus through prayer and the faith he had in Jesus'healing power.
Our faith in God, in His promises, and in His desire to have us close to Him makes Him forget our sins. It is the devil who would like us to stay in the paralyzing grip of sin. It was Satan's voice speaking in the disbelieving crowd that day, and it is his voice we hear when we try to turn from sin. The voice that tells us we are not good enough, that God could never forgive this or that sin.
It is God who wants to do things in us and for us; it is He who makes all things new. He tells us in Isaiah:

 In the desert I make a way,in the wasteland, rivers.The people I formed for myself,that they might announce my praise... It is I, I, who wipe out,for my own sake, your offenses; your sins I remember no more. (Isaiah 43: 19, 25)

Let us not weary God with our sins, but confess them, and with God and by our faith, for get them.