A god wouldn't need to send his son to die to remove our sins....he has the power to do that all by himself any time he wants.
Consider this: A man invokes a large debt to be paid at a later date. When that day arrives and the creditor is unable to be paid, the law states that the debtor must be taken to debtor's prison. The debtor pleads with his creditor to give him more time or in some other way let him pay the debt so he doesn't go to prison and lose all that he has. The creditor feels sorry for him, but the contract demands payment in full or the debtor must go to prison. One demands justice, the other mercy. To appease both, their must be a third party, the mediator. This man, a good friend of the debtor, knowing that the debtor was short-sighted and didn't think things through, pays the debt for his friend. The mediator requires that the debtor pay him back, stating that while it won't be easy, it will be possible. This appeases justice, since the creditor received full payment, and mercy because the debtor got a second chance and another opportunity to pay his debt.
Let's say that we are the debtor, imperfect and with lot of sins on our account. God, the creditor, loves us, but he can't let any sinful creature into his kingdom. Jesus Christ steps in, a perfect man with no debt who loves us and is able to pay the debt. He agrees to "pay our debt" by atoning for our sins. All we must do is agree to do as he says. Through this, we see that we can repent of our sins through Christ.
Our sins can't be immediately removed because the law of justice would be left unfulfilled. Only through Christ's atonement can we fulfill the law of justice and still be able to live with him again.