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Judaism: why kill somebody just for his claim that he is a prophet of God?
May I assume you are talking about Jesus?
If so, that isn't why he was crucified. He was executed by the Roman authorities for treason against the state. Whether it was true or not*, Jesus was executed for insurrection and not any theological claims. The Romans did not care about Jewish religion.
Now, the Jewish authorities probably despised Him for being a social reformer. That threatened their position of wealth and power. They may well have trumped up some charges to get rid of Him. The case against Him appears to have been weak, Pilate wasn't convinced at first. But Pilate didn't much care about one Jew so just ordering the execution was the easiest thing to do. And it set an example for the other Jews as they gathered in droves to Jerusalem for Passover. "Don't Mess with Rome!", is the clear message sent by such a horrible execution.
But it wasn't about prophethood or anything like that.
Tom
* I believe that it was true. I believe that Jesus was a violent antiRoman revolutionary. If He were a modern day Iraqi fighting the USA occupation He would be considered a terrorist.