The problem why you interpret that islam does not belong in the western world, is beacause a majority of muslims are very conservative/tradtional. The western world interpreted by the middle east is basically a liberal hellhole. The west isnt culturally conservative as how you interpret it. A recent study in the U.K. from the Qulliam Report(i dont know which one il need to find it) show that British muslims are much more conservative than other conservatives in the country. It also explains why there is an extreme negative view towards homosexuality, promiscuous relationships/sex and adultery, as these are still considered as part of fundemental consevative beliefs. Basically what im trying to say is that the West to a Muslim/Arab/Persian/South Asian is more of a liberal hellhole than anywhere near conservative.