I think the main reason Israel is an unsolvable situation is because of religious fervour. Zionism and The Balfour Declaration were stupid and so Israel was put in the Middle East. It should have been put in Oregon. Now we have evangelicals who believe that if Jewish settlers steal enough land they can bring on Armageddon. We have Jewish settlers willing to oblige for religious reasons. On the other side we have groups like Hamas that pay people's families if a kid decides to blow himself up in a suicide mission. None of this should be impossible or hard to solve but for the deep convictions of all these. Fact Jewish settlers believe they can bring on the messiah, fact Christians believe in the rapture and the notion of Martyrdom & Jihad among Muslims make it an impossible situation.

As for other militant groups I think much if it is religious. A close friend of mine left for Syria when I was about 19, he was a regular dude. All of a sudden he went to join a group considered Jihadists, essentially he went to help the Ummah cause the Syrians were getting fucked over by Assad. He went and then so did his brother, his brother died and he is still there so far as I know. As hard as it is to imagine I have met some people who obviously believe in paradise. Combine that with a belief in Martyrdom and you get otherwise sane people behaving like lunatics.