Also, in the case of Christ there was a human sacrifice. One may say all they want about a 'lamb's, but this doesn't change the fact. If I remember correctly, God in the OT clearly condemns this.
Now here you have what I call a "Cliff Notes" version of Jesus' work on the cross. Let's take a deeper look at the life and times Jesus lived. The Romans were crushing the Jewish nation into a poverty stricken existence. They were taking their land, making serfs of the former owners, and demanding taxes. The Temple was also asking for its tithes and sacrifices. It was a very hard time for the average Jew, unbearably so for the poor. What to do? Feed their family or follow Jewish law about Temple donations and sacrifice?
Along comes Jesus reminding the poor of Old Testament teachings: God forgives. Sins are forgiven. Repentance for the forgiveness of sins. In other words, Temple donations and sacrifices are not needed for the forgiveness of sins. Jesus said (considering the times) the Temple should not be laying further burdens upon the poor. At the time, the Temple was being led by Annas and Caiaphas, who were far from being the epitome of the ideal Jew or any type of leader showing loyalty to their own people.
The Annas-Caiaphas faction demanded a sign that Jesus' teaching of repentance for the forgiveness of sin was in fact from God, that it was in fact a covenant between God and His people. If Jesus could not provide a sign of this, then he should cease and desist in this teaching that sins ARE forgiven (not will be forgiven upon his death). Covenants were often sealed by blood, and this was indeed a sign of this New Covenant/Testament. Even more so, was the sign of the Resurrection.
I have the impression that you, too, believe sins ARE forgiven. I am guessing you can point out that sins ARE forgiven even when Temple sacrifice cannot be performed.
Jesus was never fighting against the Jewish faith. He was fighting Annas and Caiaphas and their perspective (influenced by Temple wealth and power) of how to use the faithful Jews.