The tension between Jesus' mission and the priests and Pharisees had reached a fever pitch. After Jesus raised Lazarus at Bethany, more people began to believe in Him. The Pharisees bring their case before the Sanhedrin. The answer is clear: Jesus must be stopped. It was no small thing to convene the Sanhedrin, the supreme ruling council in Israel. Caiaphas, whom we get to know later in the Gospels, issues what amounts to a prophecy about the death of Jesus "...that one man should die instead of the people." For the high priest to issue this proclamation is profound. There was no turning back. Everyone there knew what it meant. The political wheels were now set in motion that would bring about Jesus' crucifixion.
What I think Caiaphas and his cohorts had in mind was that bringing an end to Jesus, and in a humiliating way, would save the people from fomenting a de facto insurrection. There was a tacit desire to keep the peace with Rome. The Jewish leaders knew that if the Romans perceived so much as a hint of rebellion, they would act swiftly and brutally. That would of course bring about suffering, but it would also destabilize the ruling order among the Jewish people. Caiaphas would probably not survive the aftermath.
Caiaphas thinks that making an example out of Jesus, showing how the people should not be led by false prophets, would solidify the faith of the people in their ruling leaders while endearing them to the Roman occupiers. Having Jesus killed as an enemy of the state of Rome and in a way accursed by the Jews would deflate His followers. It would serve as a great example for people to keep in line, to check their worship first with the priests and Pharisees, and to refuse to follow anyone not officially endorsed by the ruling party.
How often does the thirst for power and influence obfuscate truth? We see this all the time. There is nothing new under the sun, as it were. The unjust railroading of Jesus to the cross mirrors the political and military maneuverings we have witnessed throughout history. When man seeks his own power and fame, he turns away from the living God. Yet, it is frequently under the guise of truth and piety that crimes are committed, such is the depth and horror of sin.
Jesus plunges unscathed into the depths of sin, down to the bottom of the pit of human wickedness. Indeed, He does die instead of the people. Jesus dies so that we may not die in our sins. How right Caiaphas was! Only, if he had paid more attention to the Torah, he would have realized that what man intends for evil, God intends for good (Genesis 50:20).