|Alabama-born jihadist Omar Hammami|
We actually do know how this happens in most cases, though it's harder to explain just why. What is clear is that it is not Islam that has driven these youth to terror, but their commitment to the movement that requires them to embrace an extremely violent caricature of Islam — to justify their actions. They are what French investigators of the phenomenon have called "precarious personalities," youth bursting with energy and rage who need direction and control in their lives. Some, like the Kouachi brothers, are/were orphans, others feel their parents have failed them for all or any of the reasons that children generally rebel against their parents — the parents' attitudes are from another time or even another country, and thus seem irrelevant. And the children live in societies where employment, education and other social goals seem unavailable or unrewarding, and where other outlets they've tried — becoming a rap star, playing video games, or petty crime in some of the known cases — have failed, and they'd much rather blame the society rather than themselves. Some of these European Jihadists come from Christian or even Jewish families, and even those whose parents were nominally Muslim were not raised to be devout.
In this respect, their path to terror has been the opposite of the original Afghan taliban, whose zeal derived from a skewed but dedicated reading and reciting of the holy scriptures of Islam, the Koran and the haddiths. "Taliban" is the plural of talib, religious scholar, a term which took on a special meaning in the isolated madrasas of the Afghan mountains, which exaggerated the intolerance of very rural people against modern, urban intrusions.
Because of course there are many other Muslims, more modern and worldly, who have also studied the teachings and history of their religion, but come to entirely different conclusions. Islam was a religion of war, originating in a 6th century warrior society, but became in many parts of the world a religion of brotherhood and peace and the encouragement of learning in all fields, very notably in medicine in the so-called "Islamic Golden Age" of the 8th to 15th centuries. But, like any religion, a selective reading may be taken as a pretext for bad behavior. How the ignorant, fierce taliban became useful tools for more sophisticated Muslims with other grievances against modern society is a big part of the history of Al Qaeda.