In the Gospel of John 19:12–16, Pilate and the crowd have a discussion in which the crowd eventually persuades Pilate to hand Jesus over to be crucified. The key persuasive lines are:
... but the Jews cried out, saying, If thou let this man go, thou art not Caesar's friend: whosoever maketh himself a king speaketh against Caesar. (19:12)
The first important element of this passage is that Pontius Pilate was a governor of the Roman province of Judaea, which was under Emperor Tiberius at the time. Although few details are known about Pilate, it is known that he was a Roman noble and member of the equestrian order. His position was one of a middle-level civil servant, and he served the impulsive and brutal emperor Tiberius. This means that a major motivation for Pilate was not offending Tiberius in order to keep his job (and his life, as short-tempered Roman emperors were prone to execute people who offended them). Moreover, as Jewish rebellions had been a problem for the Roman Empire, a major goal of a governor of Judea in particular was keeping order and preventing riots.
The Jews, therefore, in saying that Caesar would be offended if Pilate released Jesus, were appealing to Pilates's own sense of self-preservation. The Jews themselves, in saying "We have no king but Caesar" (19:16), are emphasizing their own loyalty to Pilate and Caesar in light of a past history which might shed doubt on that loyalty. This means that although Pilate himself was not entirely sure that Jesus should be executed on moral or legal grounds, he acted out of a sense of expediency.