John 18;31 Why did the Jews want the Romans to crucify Jesus?

 31 Pilate therefore said to them: Take him you, and judge him according to your law. The Jews therefore said to him: It is not lawful for us to put any man to death;

Cornelius a Lapide

It is not lawful for us to put any one to death. For the Romans , it appears, had deprived the Jews, as a conquered people, of the power of capital punishment and claimed it for themselves. This is the meaning of the words. See Rupertus, S. Thomas, Jansen, Suarez, and others. You will say the Jews stoned S. Stephen, and threw down S. James headlong. But this was not in course of law, but in a popular tumult. Josephus (Ant. xx8 , al16) says that Annas was deposed from his office by the Roman governor for ordering S. James to be killed, and ( Acts 18) the Jews did not dare to kill Paul, but handed him over to the Proconsul Gallio. But you will urge that Pilate had already given the Chief Priests liberty to judge and to put Him to death, when he said, "Take ye Him and judge Him according to your law." I answer, that they could have done Song of Solomon , but were unwilling to accept his offer. They said, as it were, in their minds, Ye, Romans have taken away from us altogether the power of the sword. We therefore do not wish to exercise it in this particular case. Either restore us this power absolutely, or else take your part in the deed. This they said as wishing Jesus to suffer the most ignominious death, that of crucifixion as a seditious person, and aiming at kingly power. And they wished to transfer from themselves to Pilate the unpopularity of His death. For they feared they should be stoned by the people, who were in favour of Jesus, or else be assailed by their revilings. Others reply (as S. Augustine and S. Cyril, and Suarez after them, par iii. Qust. lxvii. art4), that it was not lawful for the Jews to put Him to death at the Passover (being a solemn feast), but that it was lawful at other times. But Ribera replies, that it was specially the practice of the sect of the Pharisees not to condemn any one to death (see Josephus Ben-Gorion, Hist. Jude 4:6). They said therefore, "It is not lawful for us," under the cloak of religion.

Cyril of Alexandria

AD 444

I should not do justice, he says, if I were to subject 

to legal penalties a Man Who has been convicted of 

no wrong, and Whose doom you left undecided; but

 judge Him, rather, according to your Law, if, 

indeed, he says, it has ordained that the Man Who is

wholly without guilt deserves chastisement. It is 

not a little absurd, or, I should rather say, it is a 

subject for perpetual regret, that, while the Law of 

the Gentiles justified our Lord, so that even Pilate 

shrank from punishing Him That was. brought to 

him on so vague a charge, they, who made it their

 boast that they were instructed in the Law of God,

declared that He ought to be put to death.

The Jews used their idea of law to put to death the

ultimate innocent man but we wish to have them rule over us?