Just because Islam is a "religion of peace", the extremists can do whatever they want ?

Jihadist exist and will continue to do so because they are able to cite their claims for the need of Jihad within their holy texts. The biggest group of these guys come from the wahabi movement started in Saudi Arabia in the late 1700s. Their claims were such as that it is noble to kill a westerner and if you kill yourself in the cause of jihad you'll get 70 virgins etc. They continue to exist because they can validate their claims.