A big problem Westerners have in dealing with the sources of Islamic terrorism is the quite different sense of reality the terrorists have. For example, if you visit a Islamic radical website (or one that supports this sort of thing), you will find discussions about the many wrongs the Islamic radicals and terrorists want to put right. Aside from the usual "destroy Israel, and get all non-believers out of the Middle East" stuff, there are some rather more shocking demands. For example, Islamic radicals want Spain, or at least southern Spain, back. Moslems have not ruled any part of Spain for over 500 years. But to Islamic radicals, once an area has experienced Islamic rule, it is Islamic forever. It's a variation on, "what's mine is mine, and what's yours is negotiable."
Another big issue with radical Moslems is the Crusades. For several centuries, ending in the late 15th century, Christian armies tried to regain control of the Christian holy places in and around Jerusalem. These had been taken from Christian overlords in the 7th century, and eventually the Moslems running the area made life uncomfortable for Christian pilgrims, as well as the large native (Arab) Christian populations. The Crusades were Christians helping Christians. But to Islamic radicals, it's right for Christians to take back, only Moslems can do that.
This sense of God-given entitlement does present some serious problems when it comes to counter-terrorism. What it comes down to is that the people that are most dangerous to you, do not even acknowledge your right to exist. Moreover, this is a position that has divine approval. No argument is possible. What to do? Military commanders who are closest to this, especially in Iraq, take advantage of another Islamic radical favorite; dying for the cause and going straight to paradise. Thus U.S. Marines advertise themselves as the "Jehadi Travel Agency," and capable of quickly dispatching holy warriors to paradise. While this might seem crude, it is perfectly in line with what Islamic radicals believe and preach. To these fanatics, it's a fight to the death, and no quarter is given, or expected. That said, the Islamic radicals also advise their followers to take advantage of enemy weaknesses. Thus if the infidels try to "understand you," use that to assist Islamic holy warriors in destroying, or taking advantage of, the clueless unbeliever.
Some Islamic radicals do eventually wake up from the nightmare they have created for themselves, but even then, you cannot always be sure. Over a dozen Islamic radicals released fro Guantanamo, have later been caught (some dead, some alive) back at their terrorist ways.