Who killed Jesus? (and why?)
When considering this question we have to acknowledge some methodological problems concerning what counts as historical sources and how best to weigh the political and theological dimensions of the surviving materials.
We begin by noting the problematic nature of our sources, none of which are "neutral" and almost all are early Christian documents. We have no official Roman documents relating to Jesus nor his death. He was not a sufficiently important character to be worth noting, even though Pilate's role in the process (and the regular recital of the creeds) has made him the best known Roman official of all time.
When dealing with Christian texts about the death of Jesus, we need to recognise the likelihood that none of the writers actually knew the details, but all simply knew that Jesus had been crucified. Paul gives no story of the crucifixion, although he knows enough of the story—and assumes his readers also do—to describe Jesus' words over the Eucharistic bread as having been spoken "on the night he was betrayed" (1 Cor 11:23). Mark gives us a heroic tale that may have little basis in what actually happened on the day, and there is no reason to think the liturgical narrative known to Paul and his communities preserved any eyewitness information about the final hours of Jesus.
When the extant materials are considered carefully, it seems there are two set of authorities with whom Jesus could have been in conflict:
the Temple authorities in Jerusalem (cleansing incident, disputes over authority, etc)
the Roman imperial authorities: Antipas in Galilee, Pilate in Judaea
The NT tends to blame "the Jews" for the death of Jesus. This is most explicit in later texts such as the probable interpolation in 1 Thessalonians 2:14–16, and especially the infamous blood libel passage in Matthew's account of the passion:
And all the people answered, saying, “Let his blood be on us and on our children!” [Matt 27:25]
The early Christian tendency to blame "the Jews" for the death of Jesus ignores the stark reality of death by crucifixion, not by stoning. Anyone in the ancient world would appreciate that a person who had been crucified had been killed by imperial authority, rather than by local authorities.
We can therefore assume that Roman authority (expressed through procurator, Herodian dynasty, and priestly oligarchy) came to the view that Jesus was such a serious troublemaker that only crucifixion was a suitable penalty for him, and an effective deterrent for other potential troublemakers.
It is interesting to compare the fate of Jesus with other known troublemakers:
A rebel and murderer such as Barabbas could be held in prison, with his death sentence scheduled for a convenient time to suit official priorities.
The troublesome John the Baptist had been detained in prison by Herod Antipas, who had little compunction about killing his opponents including members of his immediate family suspected of disloyalty.
Paul would later be arrested/imprisoned and subjected to various physical punishments.
However, Jesus is arrested and executed within the space of less than 24 hours. The speed of the execution, as much as the method, indicates the anxiety of the Roman authorities. If the passion narratives are to be believed on this point of detail, then the speed of his despatch tells us a great deal about the political risk factors at work in the case of Jesus.
Once again, we need to reflect on the nature and quality of our sources. It is common to consider Mark's account to be historical, but perhaps it is better to see Mark's account as a narrative expression of Christian theology ca 70 CE. Mark has a specific agenda in representing Jesus as the innocent and heroic victim of city authorities, but there is no compelling reason to think that Mark had access to any reliable information about the details of the arrest, trial and execution.
Methodologically, I exclude the narrative details found in Mark and his imitators (Matthew, John, and Luke). It seems wiser to base our argument only on the core event: a hasty crucifixion, with a focus on Jesus rather than his followers. Jesus was detained and killed with almost no time spent in detention. His followers were not arrested, and there seems to have been no systematic attempt to suppress the Jesus movement.
Overall then, it makes sense to see Jesus within the matrix of rebels and messianic pretenders in the Jewish territories at the time.
For original sources relating to these political uprisings, see the following pages from Mahlon Smith's Into His Own web site:
While Jesus' followers insisted he had no messianic pretensions, that was not how the authorities saw him. Operating within the Roman empire, it is not surprising that the earliest Christians played down messianic rebel tag. Given the polemical situation between the emerging Christian and Rabbinic Jewish communities after 70 CE, it also makes sense that they would deflect responsibility for the death of Jesus onto Jewish leaders and exonerate Rome. Such an approach to the problem of Jesus being crucified was part of a consistent Christian "spin" to gain leverage off the Jewish rebellion and to portray themselves more positively in the eyes of the Roman authorities.