It would be a mistake to believe that life in the Middle East was less complex in the first century than it is today. Today, it is oil that turns the wheels of political and commercial intrigue, but back then it was food. The eastern provinces of the Roman Empire, especially Egypt, provided the necessary food supplies to keep Rome living in abundance and luxury, while the rest of the world struggled to get by. The province of Syria, which included Galilee and Judea, provided the needed buffer for Rome between its control over the rich provisions of Egypt and any threat from the Parthian Empire, further east (largely Iran today), who would also have liked to control the Middle East.
So, why do the forty Jewish men volunteer, without being asked to do so, to hazard their lives to kill Paul (Acts 23:12-13)? The Jews had become increasingly unhappy with their Roman governors. The desire for independence and self rule became progressively more evident and the decade of the 50s in the 1st century CE saw the rise of many zealot groups who not only waged occasional war with their Roman lords, seeking to ignite full scale rebellion, but also sought to punish Jews who seemed to encourage or sympathize with the Roman presence. The accusation against Paul that he brought a gentile into the Temple would not have been overlooked or taken lightly by any of the zealot groups who were probably present at the Festival of Pentecost.
Moreover, the fact that Ananias had Paul struck when he appeared before the Sanhedrin, saying he had lived in good conscience before God (Acts 23:2), seems to imply the Jerusalem authorities were very current on Paul’s activities in the Diaspora and very sensitive to his mingling Jews with gentiles in what appeared to them as blurring the clean and the unclean. So the Jerusalem authorities and the Jewish zealots considered Paul a common enemy and would have worked together to eliminate the threat they saw in him to their Jewish identity.
Josephus tells us that Jonathan, the high priest, was murdered in the Temple by these same or very similar zealots who were secretly bribed by Felix, the Roman governor of Judea, because of Jonathan’s too frequent interference in Felix’s affairs. And, one has to wonder if this was not at least partially due to the obsession of the Jewish authorities to have Paul extradited to their custody for trial and eventual execution (cp. Acts 24:6-7, 27; 25:2-3).
Therefore, when the plot against Paul’s life was found out by the Roman tribune, Claudius Lysais (Acts 23:16-22), he had Paul removed from the Antonia at Jerusalem to Felix’s headquarters at Caesarea. No doubt he gladly transferred Paul’s custody to Felix, not only because he was unable to ascertain why the Jews tried to kill him, but also, if he was unable to keep a Roman citizen from harm in the Antonia, it certainly wouldn’t have looked very well to his superiors. However, in writing a letter to Felix, he was able to put himself in a very good light making himself responsible for uncovering the murderous plot against Paul. He also made it appear that he was rescuing a known Roman citizen and conveniently left out that he nearly flogged Paul and publically had a Roman citizen placed in chains (Acts 23:26-30; cp. 21:33 and 22:24-29).
Felix questioned Paul, asking what city he was from, perhaps willing to extradite him there, but, when he found out Paul was born in Tarsus, he decided he would hear Paul’s case himself. Tarsus would have come under the responsibility of Felix’s superior. To extradite Paul there would not only make it more difficult for Paul to face his accusers, but the President of Syria, Felix’s superior, wouldn’t have appreciated having to take responsibility for something that should have been handled by Felix, himself.
 Josephus: Antiquities of the Jews 20.8.5