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.
The rest of your post is nonsense. Exporting Western commercial products isn't exporting Western "culture." Nor did Bush claim that anything more than a general desire for freedom motivates mankind. He may or may not have been right about that, but if he was or wasn't, liberty is hardly an aspiration unique to the West.
The problem with Western Civilization is that it doesn't believe in itself anymore, not that it's too aggressive in advancing its agenda.