I'm assuming you mean the "political" or "social" reasons Jesus was killed as opposed to the theological significance or motivation of his death.
Recall that the Judean state had been in tumult since the Maccabean period. The expectation of many Jews for a political "Messiah" (i.e. someone "anointed" to reclaim the throne of David) was at odds with the imperial power of Rome. When Jesus proclaimed the inbreaking of the "kingdom of God/Heaven" he was making a political statement over and against the "kingdom of Rome." This is why the disciples ask Jesus:
Lord, are you at this time going to restore the kingdom to Israel?" - Acts 1:6
They were expecting Jesus to destroy the Romans and reestablish the Davidic kingship. This is also why it was so confusing for the disciples that Jesus would be killed—especially after, for example, the triumphal entry, which imitated (or mocked, depending on who you ask) a General returning to his city from a victorious campaign. The Qumran community had basically the same Messianic understanding, except they expected two messiahs, one a political leader, and the other a priestly figure. The two Jewish revolts after Jesus also provide nice examples. The first, Rome crushed in 70 CE with the destruction of the Temple in Jerusalem, and in 74 CE at Masada. The second, in 132-135 CE ended with the death of Simon bar Kokhba, the rebel leader.
As such, Jesus was arrested and killed essentially for for sedition--the Jewish leaders who were collaborating with Rome wished to keep the peace, and the best way to do that was to silence dissenting voices. The whole "claiming to be God" bit was really more of an excuse (or anyway, according to my understanding of the text).
I would also caution placing too much blame on "the Jews," that is, "the Jewish people," since the Jewish leadership was a very small and powerful group of elites. Parts of the NT (particularly GJohn) border on anti-Semitic at times, but we should be sure to consider the historical sitz of such writings and understand that it likely is a reflection of tension between Jewish and Christian groups in the late 1st/early 2nd centuries, and not necessarily perfectly historically accurate.