Correction: It is your BELIEF that certain Jews agitated for the execution of Jesus. It is not proveable fact.
Look, that's the story. None of the story is "provable fact" but why should that matter.
Just as it is your BELIEF that Jesus even existed? Please; spare me. The same documents upon which you predicate your belief in the earthly existence of Jesus inform me that certain Jews agitated for his death. It's not scandalous that they should have done so; indeed; it was quite understandable. Jesus was obviously a very popular individual whose presence could incite other Jews to insurrection. The leading Jews feared Roman retaliation, and indeed they had good cause to fear it, as witnessed by the events of 66-70 A.D., fully outlined by the historian Josephus. It wouldn't necessarily have been out of malice or ill will that they acted against him; simply a fear that everything they had would be destroyed by Roman retaliation.