Saudi Arabia has spent billions of dollars to export this type of religious school. Government supported religious charities have built thousands of mosques, which often have madrasses attached, and subsidized the living expenses of religious teachers. Often, the madrasses hire radical teachers from other Moslem countries. The Taliban started out as students in Pakistani and Afghan madrasses, with many of their teachers leading them in battle. The madrasses teachers tend to believe in what they are preaching, which makes them even more dangerous.
While this Islamic radicalism is a fringe movement, with only a few percent of Moslems really into it, that's still over 30 million people who believe in this sort of thing. And since the Islamic radicals are encouraged, by their interpretation of the Koran, to use violence in defense of their beliefs, they often intimidate more moderate Moslems into either supporting them, or just standing aside. Governments have to be rather brutal to keep the local Islamic radicals under control. Europe, which is quick to condemn such tactics, is discovering that the radicals among its own 20 million Moslems, are very difficult to deal with.
Mainstream Islam disagrees with the radical version taught in these Wahabi madrasses, but there has been no widespread effort to crack down on these schools. There is the belief that eventually the radical madrasses will go away. But the history of Islam shows that these radicals have always been around, and every few generations they get really violent. While that violence may pass, the radical tradition that brought it about is still there, and will surge again in the future.
The most frequent source of Islamic terrorists is a place that counter-terrorism organizations have a very difficult time reaching. That would be the thousands of madrasses (religious schools) that teach the Wahabi (and related) interpretation of Islam. Wahabis believe that infidels (non-Moslems) are the cause of all the world's problems. The solution is to convert or kill all the infidels. That's it. A simple message. All the rest is just lots of anecdotes reinforcing the basic message. The radical madrasses don't teach terror, which makes them hard to shut down, but they do emphasize the need to struggle, even die, in order to serve Islam as best you can. Saudi Arabia, where Wahabism developed in the 18th century, tries to get the madrasses faculty to lighten up a bit, and at least point out that terrorism is un-Islamic. Not surprisingly, many of these madrasses teachers refuse to back down when it comes to delivering a hard core message. They are on a mission from God. Saudi Arabia has dismissed some of the more extreme teachers, and even jailed a few. But those who can no longer teach openly, while on the government payroll (Saudi Arabia pays the salaries of all clergy and religious teachers), do it on the sly. In other countries, attempts to shut down pro-terrorist madrasses has been difficult, because the religious teachers scream persecution, and accuse the government of being an enemy of Islam. Since these madrasses don't teach logic or critical thinking, they can usually get their students out in the streets, to protest the closure efforts.