Accepting the original gospel of salvation by faith, "takes away the sin of the world". His willingness to come down from the glory of heaven, live the difficult human path was a "sacrifice".
The Jews used to have to sacrifice animals twice a day by the priest and people individually brought animal sacrifices. That was God's commands. Jesus came to earth knowing he would be the Sacrificial Lamb of God.
You should stop ignoring the fact that Jesus taught his gospel before the cross, he had hoped the Jews would receive it, they didn't. Rejecting and killing Jesus became the new gospel as it was understood through Pagan minds.
The Jews were not pagans. The Jews atoned for their sins the way God told them to when He gave Moses the Law.
The old Law was NOT based on faith. It is why God did not like it when the people would sin, do a righteous act of giving a sin offering, but not really be sorry for their sins. God said a New Covenant was coming where He would atone for the people's sins, those He choose.
When Jesus came to earth, God cut off and hardened the Jews who did NOT already belong to Him by faith. God was making a New Covenant that was based on faith, surely He is not going to cut off those who already have faith. Those Jews who already had faith were already saved, but they needed to repent of their sins; they were God's people and now they had to go through Jesus to remain the Father's.
The Jews who did not have faith in God but were merely enforcing the Law and cleaning themselves by doing the purification works...they were cut off and hardened when Jesus came. After Jesus was killed/sacrificed, then all could come to him to be saved, Gentiles and even the cut off and once hardened Jews.
There were many Jews though who could not accept that Jesus' blood washes away their sins and they wanted to keep cleaning themselves the way God in the Old Testament told them to do it.
Jesus came first for those who already belonged to God by faith, they were God's and He gave them to Jesus. They now had to go through Jesus. Jesus said he would not lose one that God gave him.
The only thing Jesus said about the cross was that it was proof of his authority to teach his gospel which many religious people hated.
What?
Jesus will continue to preach his original gospel to those open minded, and open hearted enough to receive it. It will eventually win. Primitive Christianity will fade away.
All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness.
People such as yourself who think they are too intelligent for the Truth start to make up their own truth; which is really no truth at all.