It isn't the "West" that they hate. They are an Islamic movement. They hate anything not Islamic in general and anything Jewish or Christian in specific. The West just happens to have the greatest degree of Christian influence in it's culture, and America is the (only) nation that developed specifically from Christianity. India, China, Japan, Russia, etc., are also targets of Islamic activity, but they are curreently minor targets compared to the West and (specifically) America and Israel.