Here's the deal. Terrorists are the enemy and terrorists will say and do anything to justify their actions. Islam is also practiced by a peaceful nation, Turkey, a member of NATO who is not hung up about recognizing Israel or Israel's right to exist. Since the terrorists purport to follow Islam, and since Turkey follows Islam your obsession with putting all of Islam under one umbrella is flawed.
Oh wise one, how would one go about defeating Islam? Exactly.
I think its past your bedtime. Let the grownups handle international relations.