Christians often assume there is a link between sacrifice and the assuaging of God's anger. It is certainly the case that the Old Testament and New Testament talk a lot about God's anger as well as about sacrifice. But they never bring these two together. Leviticus, the book that tells us the most about sacrifice, never mentions God's anger in this connection. Insofar as sacrifice deals with problems, the problems are the need to be made clean and the need to make compensation for wrongdoing.Fuller: Theology, News & Notes. VOL. 59, NO. 2.
Isaiah 53 speaks of God's servant offering his life as a compensation offering to God, and also of his bearing our punishment. Oddly enough, neither of these two lines is quoted in the New Testament, unlike much of the rest of Isaiah 53. . .when Christians think of Christ bearing the punishment for our sin, they are thinking of the punishment meted out by a law court for wrongdoing, but this is not the regular connotation of this word, nor the connotation suggested by the context in Isaiah 53. The servant of God in Isaiah 53 is going through chastisement all right, going through ill-treatment at the hands of his own people and/or at the hands of the imperial authorities, but he is not going through a judicial punishment that other people thereby escape.
The ordinary meaning of the Hebrew word most commonly translated "forgive" is "carry." It is what parents do for their children's wrongdoings and what God was doing with Israel through Old Testament times. It was a process that came to its climax with the cross, which is the logical end to the Old Testament story. Seeing the way the relationship between God and Israel worked helps us see why the cross was necessary. Through God's life with Israel God was paying the price for that relationship, making the sacrifices to keep it going (my own note: we see this in Hosea).. God's people keep doing their worst to God, so eventually God paid the ultimate price for them. God showed that even killing God cannot put God off from relating to them. God will just come back from the dead.