Let's say that I am at your house and we are having a discussion about the nature and extent of the atoning work of Christ. In my excitement, I knock over a lamp and break it, but you are a gracious person, and you forgive me for my offense against you. However, you then require $10 as payment even though you have forgiven me. Is it true forgiveness to require a payment for what you have forgiven? Of course not. But the lamp needs to be replaced. So, in true forgiveness who is left to pay for the replacement of the lamp? You are (now in a real-world situation I would, of course, offer to replace it, but this illustration is meant to exemplify what true forgiveness really is as it relates to payment). If I were to pay for the replacement of the lamp, a payment has been made and you, the owner, are satisfied. With God, we the lawbreakers are not capable of making a sufficient payment to rectify our sin problem because our righteous deeds are filthy rags before God (Isaiah 64:6). Since we are not capable of making a sufficient restitution payment, the only one left to do this is God. Therefore, logically, God must be the one who makes the payment just as you, the lamp owner, in true forgiveness, would pay for the replacement of the lamp. God is the one who is offended by our sin against him, yet He also forgives.  But His forgiveness does not negate the necessity of the law being administered because the law, which is a reflection of the character of God, states that he who sins must die (Romans 6:23). Sin is breaking the law of God (1 John 3:4), and God cannot arbitrarily dismiss His law, otherwise, He is not just. So, He takes the law upon Himself via the transference of our legal debt to Himself on the cross and dies with it. Therefore, the law is satisfied, and we are forgiven.