I'm guessing you left out something significant in the ellipsis, since the second part of this statement is not the least bit true. Western intellectuals and their sheep don't believe in any obligation to extend their culture throughout the world. Far from it.
But of course the West has been aggressively (or substitute "assertively") extending its culture for 500 years. Every time George W. Bush opened his mouth to talk about Iraq and Afghanistan, he was reminding us that we are extending the ideals of constitutional government, regularly scheduled elections, freedom of the press, speech, religion, all men are created equal--- all these taken as universal norms.
Others want to extend a level of material culture: iPods, WiFi, cars, weapons, beef, beer, running water, flush toilets, Disney World and porn. All those billions in advertising/marketing dollars aren't going for nothing, you know.