Pilate said, “Take him yourselves and judge him by your own law.” “But we have no right to execute anyone,” the Jews objected.
Pilate does not want to be manipulated by these Jews. If there is no offense against Roman law, then they must try Jesus themselves. The Romans respected the local laws of their conquered nations and allowed them a great deal of autonomous judicial administration. However, they did not allow their conquered peoples to have the power of a death penalty. This was because they didn’t want a conquered people to have the power to kill those who collaborated with Rome. Jewish tradition has it that the right to inflict the death penalty was taken from them 40 years before the destruction of the Temple. The stoning of Stephen was illegal, but probably not punished by Rome since it was a popular act. Jesus, however, had a great deal of support among the people and the Jewish leaders would have been very reluctant to test whether Pilate would punish them for killing Jesus.
Matthew Henry notes that since they have not the power to put anyone to death, it is evident that the scepter had indeed departed from Judah as is spoken of in the prophecy in (Gen 49:10) and yet none of them asks the whereabouts of Shiloh (“he to whom it belongs”).
Genesis 49:10 The sceptre will not depart from Judah, nor the ruler’s staff from between his feet, until he comes to whom it belongs and the obedience of the nations is his.
There is another reason that the Jews wanted Rome to kill Jesus. It would place the blame on Rome and not on themselves.
Pilate rather slyly gets to the bottom of the matter in that the Jews did not want justice to be done, but a death sentence handed out. Note that the insolence of the Jews has died rather quickly now that it seems they might not get what they want from Pilate.