Who is responsible for the death of Jesus?
Most classical historians agree that it is Jesus, himself, who is responsible for his own death.
Although he fell at odds with the Court of Jewish law in the Great Temple of Jerusalem and was subsequently arrested by Jewish soldiers in Judea, it was his own wrong-doing that caused the Jewish Court to find him guilty of Blasphemy, in that he said that he "is the Messiah", in addition to all of his other "rabble-rousing" and "trouble-making" in Judea, which certainly did not go unnoticed.
According to Jewish law, blasphemy is punishable by death.
HOWEVER, since Judea was a Roman Province, under the watch of Pontius Pilate, the Governor ---- it is Pilate, and ONLY Pilate who could have condemned Jesus to death.
In all provinces of the Roman Empire, the right to put anyone to death fell within the decision of the Governor of (that) province. NOT to anyone else.
When the Jewish soldiers turned Jesus over to Pilate and said that "he is guilty of blasphemy" --- Pilate's response was: "This man has not broken any Roman law". However, in a moment of inspiration, Pilate then asked Jesus: "Do you consider yourself a 'King'". Jesus' response was: "Yes, but my kingdom is not of this world". THAT was enough to satisfy Pilate that Jesus should be excecuted, because he NOW broke Roman law --- NO ONE, except the Emperor, was allowed to call himself "King".
Thus, by his own hand, his actions and words --- it is Jesus, himself, who is responsible for his own death.
Let us put to rest, once and forever, that it is NOT the Jews who killed Jesus. This was Pilate's decision, based upon Jesus' own words that "he is a King" ---- against Roman law.
The Temple-based Sanhedrin at that time was riven by internal strife. A major contingent of the court had been corrupted by the Priesthood, which had itself been corrupted for close to a hundred years by then (once the Hasmonean dynasty had been trapped by the subjugation of Rome, and begun its collapse, ending in its eventual supplantation by the Roman-pawn Herodian kings, who were not Jewish, but readily corrupted every Jewish institution they could).
The contingent within the Sanhedrin that was not corrupted refused to work with the Roman government. Thus, at that time, they were refusing to hear any capital cases, lest the verdicts be tampered with, or lest the condemned be taken by the Romans to be executed in a manner not in accordance with Jewish law.
Jewish law prescribes and permits only four methods of execution: stoning (either the condemned was buried to the waist and pelted with heavy stones until dead, or was thrown over a sheer cliff, and a large boulder dropped on top of him), burning (not at the stake, but rather, molten lead was poured down the condemned's throat, killing him instantly), beheading by the sword, or strangulation using the garrotte. In all cases, the full Sanhedrin was necessary to condemn, by a majority of at least two votes, and only after eyewitnesses testified that they had seen the accused commit the capital offense, but they had warned the accused not to commit the offense immediately prior-- a warning which the accused had to acknowledge verbally. Regardless of the method of execution, all condemned were drugged or made semi-conscious with drink before execution. Death had to be quick and as painless as possible. If condemned to death, it was forbidden to beat or flog the criminal before execution.
Therefore, if there were indeed a session of the Sanhedrin at which Jesus was convicted of any capital offense, and handed over to the Romans for them to execute, it was by definition an improperly convened and illegal proceeding. Which means that it would only have been done by an illicit partial court, who were knowingly and openly violating Jewish law.
It is also worth noting that under Jewish law, it is not blasphemy to claim that one is the messiah, even if one is not the messiah. It may be fraud, and it may be perjury if done under oath. But it is not blasphemy, at least not in the capital sense. There were hundreds, if not thousands of guys running around ancient Israel in Jesus' time claiming to be the messiah. None of them were accused of blasphemy, much less put to death for it, although the Romans did tend to kill off those that looked like they might want to start a revolt. If the one claiming to be the messiah is also attempting to persuade fellow Jews to break the commandments and fail to observe Judaism properly, that may be heresy, and false prophecy. But it is unclear from the gospel texts as we have them that Jesus indeed failed to keep the commandments, or caused other Jews to do so: such inferences to the effect that exist in the texts may well have been Pauline additions, or other corruptions of the actual events. Personally, I doubt that he would have done so: he seems to have been a reformer, with very unorthodox ideas, but not a true heretic. I personally believe the heretical elements were added to the story later, by non-Jews.
But in any case, it was only the Romans who crucified people, as crucifixion is forbidden by Jewish law. It was only the Romans (in that area) who whipped and beat condemned prisoners before execution. It was only the Romans who were executing people at all, and it was only the Romans who had reason to fear anyone claiming descent from King David. Pontius Pilate was known, from his prior postings, to be both vicious and ruthless, not to mention overly fond of crucifying people.
I personally think that it was simple: the corrupt High Priesthood feared Jesus' popularity as a reformer. The Romans probably disliked any descendant of David who had a largish popular following. The corrupt Priesthood convened an illegal show trial (and, by the way, the Priesthood had no legal power to convene a Sanhedrin), assembled a small "mob" of paid goons and corrupt cronies, and gave Pilate the excuse he was looking for to indulge his taste for cruelty. The whole process probably had nothing to do with the real Jewish authorities, and most Jews probably knew nothing about any of it.
It is also worth noting that, while Jesus does seem to have had a popular following that numbered in the thousands, most Jews had probably never heard of him, and cared nothing about him or his followers or his preaching. Charismatics, wonder-workers, faith healers, would-be messiahs, mystics, and reformers were all a dime a dozen in those days. The truth is that the vast majority of the Jewish people had nothing to do with Jesus, and never heard of him until Christianity started becoming a thing. And that only began happening when non-Jews began becoming Christians in large numbers without first converting to Judaism.
The stories in the gospels were written by Jesus' followers and their disciples: they wanted to believe that everybody was caught up in the events that they felt had changed everything. And so they wrote the gospels that way. But that was just their own passionate beliefs speaking. Jesus only became of interest to the Rabbis when his followers began to try and persuade observant Jews to consider him more than human, after he was already dead. And Jesus was entirely insignificant to the Jewish people at large, right up until the point at which his non-Jewish followers began to harass and oppress the Jewish people.
The Jews didn't just not kill him. The Jews didn't even care. He was just one more nice Jewish boy killed by the Romans...like a thousand others.
