There's a big difference between having a debt cancelled and a debt paid for.
When a debt is cancelled the cost is absorbed by the one who is owed the payment. When we trust Yeshua (Jesus) the Father cancels the debt because he is gracious. Bringing a person to God cost the son something, but it also costs the Father something.
We cannot be right with God while we refuse to trust him.
Yeshua died on the cross to draw all men to Himself. He died so that men would trust him.
Dying on the cross is the greatest price Yeshua could possibly pay. But he did not die on the cross to make a payment to the Father. (Martin Luther certainly didn’t believe that the Father’s wrath was poured out on the Son, and neither did the early Christians. See Christus Victor by Gustaf Aulén. Nowhere in the Bible does it say that Yeshua died "to pay the debt owed to the Father." That idea has been read into the text by certain well meaning but misguided theologians. Though it is true that when we begin to trust Yeshua God's wrath is appeased.1)
The Father offers us forgiveness on the basis of trust; on the basis of faith. Biblical faith simply means to trust God. It means to take God at his word (that he cares for us) and then set about doing his will. (Trusting the Messiah also includes obeying the Messiah. See Trust).
It's impossible to be right with God while a person refuses to trust God. (This has always been the only way to be made right with God. Trust is always reflected by obedience. See James 2:26 and Ezekiel 18.)
"But God cannot look upon us because of our sin."
That kind of thinking comes from a mistranslation of Habakkuk 1:13. Most translations today accurately translate the first part of the verse.
"Your eyes are too pure to approve evil, And You can not look on wickedness with favor. " (Hab 1:13a, NASB, emphasis added)
God is extremely patient. He sees all our sins and loves us still.
"But doesn't our righteousness have to surpass that of the Pharisees to enter the Kingdom of God?"
The Pharisees of old were not trusting God. They thought His love could be earned. Their starting point was doubt. Their starting point was disbelief. God's love cannot be earned and it cannot be lost. The person who thinks God only loves people who are good doubt his goodness; this is not pleasing to him.
Yeshua came to save us from sin. When we start trusting and obeying the Messiah we experience God’s forgiveness and have begun to be saved from sin. If a person admits to their sin, thanks Yeshua for dying for them, and then swears allegiance to him as their right ful king, they have repented. Repentance is their first act of obedience; salvation has begun.2 (We are called to a life of repentance. Those in Christ will discover sins they are not yet aware of and repent of them. They will become more and more like the Messiah. They will overcome. See "Salvation from Sin" in The Hope of the Gospel by George MacDonald)
"But even if God sees all our sins, don't we have to be perfect to be accepted by God? He will not tolerate sin."
It's true that he will not tolerate sin. But why does he hate our sin? Does he hate our sin because he's Holy? Or does he hate our sin because he loves us? (It's his love that makes him Holy.) He hates our sin because he loves us. He hates sin because sin destroys us. His wrath burns because of his love. That's why God sets about destroying our sinful nature the moment we begin to trust Yeshua. (See Perfect.)
"But doesn't justice require punishment for past sins?"
Good question. It's time to take a closer look at the doctrine.
What's Wrong with the Innocent Dying for the Guilty?
1. Yeshua always perfectly trusted the Father. He was the only one who ever paid all that was owed to the Father--perfect obedience. Jesus meant nothing more than this when he said, "It is finished." When Jesus said those words he was not saying that he has paid our debt to God.
2. “It is the one terrible heresy of the church, that it has always been presenting something else than obedience as faith in Christ.” - George MacDonald