Jesus wasn't a Christian – that word exists for his followers and came later. He was Jewish. His mother was Jewish. He was circumcised as a Jew. He pretty much followed the Jewish law, departing from it only in the name of what he saw as its deeper meaning. "For truly I tell you, until heaven and earth pass away, not one letter, not one stroke of a letter, will pass from the law until all is accomplished," he insisted at the end of the Sermon on the Mount. Sure, he debated furiously with the Pharisees and Sadducees, especially about the significance of the temple. And, in time, this argument came to be restyled by Jesus' gentile followers as an attack upon Jews per se. But originally it was an internal debate within Judaism, not an attack upon Jews from the outside. In was an internal debate in the same way that the prophets of the Hebrew scriptures, such as Jeremiah, often attacked the priests of the temple for missing the point.

It is a horrible irony, then, that Christianity bears primary responsibility for historic antisemitism. Few ideas can have been as poisonous as, and inspired more murderousness than, the idea that Jews were the Christ-killers. Of course, only the Romans had the legal authority to crucify someone: it was their signature way of dealing with troublemakers. But this fact became historically inconvenient for a religion that was eventually to place its global headquarters within Rome itself.

So what, then, about this unpleasant video recently released by the evangelical organisation Jews for Jesus, and widely dubbed as one of the most offensive religious videos ever made? Already watched by more than a million people, it shows Jesus, carrying a cross, being selected by Nazi guards for the gas chambers. "Just another Jew," the guards sneer. Given the history of Christian antisemitism, using the murder of 6 million Jews as a pretext for converting Jews to Christianity is mind-bogglingly offensive. As Jews commemorate Yom HaShoah on Sunday, the only proper Christian response to the Holocaust ought to be one of contrition and an acknowledgment of the ways in which Christian antisemitism prepared its ideological ground.

Instead, the film That Jew Died for You uses the Holocaust for Christian propaganda, ending with a quote from the book of Isaiah that evangelical Christians have long used to explain the meaning of Jesus's death on the cross: "But he was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought us peace was on him, and by his wounds we were healed."

The idea here is that Jesus's death is a punishment by God for human wickedness. He pays the price of human sin on our behalf. This understanding of what Christians mean by salvation – known technically as penal substitutionary atonement – was actually unknown in the early church, though some Christians seem to think it is the only way of understanding the cross. They ignore the fact that it transforms God into some sort of psychopath who murders his own son as a magical way of dealing with endemic human wickedness. When set in the Holocaust, it doubles the offence by implying that the gas chambers are also a sort of payback by God for human wrongdoing.

Even in terms of Christian theology, penal substitution is a mistake, not least because it doesn't give the resurrection any work to do in the economy of human salvation. Indeed, there are multiple other readings of the cross, which do not rely on this payback model but, out of respect, I am not going to go into that here. While Christians regard the cross as an inevitable part of human salvation, for Jews it remains a symbol of centuries of oppression. And the right and proper Christian response to this is a confession of complicity, not a trumpeting of theological superiority.

Twitter: @giles_fraser