I don't know how it happened, but the other night at my Bible study the question of what it means that "Jesus died for my sins" came up. I ended up deliniating a few views of what the cross means in the New Testament and over the centuries. It genuinely seemed to surprise some people that the view of Christ as a substitutionary punishment isn't the only view in the Bible and elsewhere. I also wanted to make a distinction between Christ being a substitute and Christ being a sacrifice. For what it's worth, I think that there is plenty in the NT that affirms a view of Christ as sacrifice. However, it is much less clear that Christ was acting as some sort of substitute, dying in our place and taking our punishment.
The idea of sacrifice as practiced by the Temple and in Leviticus had more to do with making an offering to God in order to restore or maintain a proper relationship between God and the people. The animal(s) sacrificed are not understood to be dying in someone's place...it's a gift offered to God in thanksgiving or in penance. Beginning in Exodus and on down through the centuries, the Passover lamb isn't understood as a substitute for human blood...it's a proper offering so that the people would be preserved by God. So when Jesus is given this term by John and others, he becomes the new offering of preservation, not a substitute.
So if Jesus is to be understood as a sacrifice, it is in that he offers himself on behalf of the people to restore or maintain a relationship. And in various places, Paul and the writer of Hebrews in particular understand it in this manner. But there is less warrant for "God needed to punish someone, and Christ satisfied Him." It's less about Jesus being punished and more about Jesus being a sacrifice, a self-offering. Maybe it's a subtle difference to some, but it's an important one, I think.
And that's alongside other understandings of the cross/resurrection in the NT, including but not limited to Christ conquering death, Christ paying a ransom (who's holding who hostage?), Christ as moral example, and Christ correcting Adam's disobedience. Sacrifice is hardly the only theme.
Also notice that the arguments for sacrifice come while people are making specific arguments. Paul brings it up while trying to get a an emerging Jewish-Christian community to accept Gentiles. The author of Hebrews brings it up while appealing to a people familiar with Temple sacrifice, trying to show that Jesus is the New Sacrifice for all time, 1 John makes him an example of self-sacrifice to be emulated in striving to love others. So there are specific reasons for Biblical writers to make this argument.
Furthermore, a substitutionary view assumes that humanity has a particular problem: estrangement from God by sin, and God's call for punishment. If this was the problem in Jesus' time, there does not seem to be much indication from people around that time where people were sitting around saying, "Guys...God really hates us right now. We've sinned a lot, and we need to make things right. How do we do that?" If this was really a problem in the way that people interpreted Christ as solving, then they didn't seem to be too aware of it until after the fact. It would be like someone walking into my house and rearranging my kitchen cupboards, leaving, and then calling me from their home and saying, "Hey, your dishes weren't organized very well, but I came in and ordered them better for you."
It seems to me that the problem of Roman occupation and regulation was much more a pressing concern. Whether that arose out of a sense of such occupation being God's punishment
However, if people were beginning to discover that a community could be formed around Jesus' life and that it could be a community without traditional boundaries, then suddenly arguments needed to be made where Christ somehow took care of any sorts of hindrances to belonging...thus, his death in certain places of the NT is interpreted to either cover any sort of identity differences and superceded past ideas of law and sacrifice. And that's what the NT writers, in part, end up doing. That's also how Jesus' language of the kingdom, or empire, of God, would have sounded so controversial and revolutionary. Smack-dab in a different empire, THE empire, he would have been advised to watch what he said. So Jesus does recognize a different problem than sin, or to put it a better way, still sin but characterized in a different way.
And the solution does in part become sacrifice: of ego, of traditional boundaries, of traditional thoughts about who can be "in," and even of one's life in order to do right by God and one another. To take up the cross as it were. But hear the good news: Christ is risen. And his--and our--sacrifice is worthwhile, if for no other reason than that God's grace is completely revealed through it.