Why exactly did the Jews kill Jesus?
Based on my reading, Palestinia had historically been a particularly difficult province to govern and was prone toward rebellion. In order to help ease the administration and keep the province from being a money-sink (legions were expensive), Roman governance allowed a lot of the traditional structures to stay in place to help keep a rebellion-prone people somewhat placated.
This Jesus guy shows up, starts gathering crowds and disrupting the status quo. Obviously the Romans had no control of him, but neither did the traditional Jewish power structures that the Romans allowed to stay in place specifically to prevent this very problem.
It looked bad. This guy had a pretty strong support base in Galilee - the very same place the last few rebellions popped up. It was a place that was a little more tolerant of radical, new ideas in the province - especially as this Jesus guy wasnāt the only one with radical sects behind him at the time in that area.
But Jesus of Nazareth got
too popular. And he was talking about new kingdoms and restoration and a bunch of other buzz-words the authorities didnāt like to hear. The Jewish control structures (which again existed to prevent this kind of thing) couldnāt readily contain him and were scared of being done away with for their failure. Moreover, there was fear that yet another uprising would occur, markets would be disrupted, more military money would be spent on a province that didnāt yield much in taxes anyway.
Ergo the real Roman authorities and the puppet Jewish authorities conspired to put an end to him and his sect before it led to much real trouble. He was accused of a bum crime, both sides claimed the other was responsible for the charges (common practice) and he was executed in a manner that was popular at the time due to itās particularly grisly nature.