The thing that people find offensive about America remaking things is that it is done as a substitute for actually ACCEPTING those foreign things. There is no reason that the originals couldn't find even wide acceptance in the USA and be left at that. The Japanese don't have to remake Armageddon to love the crap out of it. Australians don't have to remake King of Queens in order to enjoy it. Those things are accepted as what they are and left to be that way.
But typically, distribution rights in the USA are sold on the condition that remake rights are as well. And the way that globalisation and multinational corporations work, even non-American films probably lead back to some office in Hollywood. This is what's offensive. While the rest of the world actually watch foreign film all the time, perhaps more than their own domestic film (and seldom bat an eyelid or even think of that as strange), the USA continues to flood the world market with its own works and leave little room in their own country's cinemas, TV scheduling and store shelves for other works of merit from overseas
That is, unless it's a 'retrospective' just in time to hype the release of a remake.
Essentially it's American Exceptionalism, the idea that the nation is number one, unbeatably unique, and OF COURSE these things would be better if more Americans were in them. And unsurprisingly, this gets the goats of a great many non-Americans who are sick of seeing their local film and television reduced to being just marketing for American remakes. The salt in this wound is that, these same people probably find barely enough room left in their own cinemas for works of their own!
An example which comes to mind is in Korea, where regulation demanded that cinemas support local film to a particular percentage each year. This gave rise to the Korean film industry explosion, but the USA got this regulation significantly reduced for their FTA, and there were protests and strikes. The thing is, Hollywood films are like many other things fast in America: they are sugary, fatty, way more than you need and are generally bad for you. But that sells because it hooks right into some primitive core in the brain that craves that kind of quick and dirty pleasure. Cinemas want to sell tickets more than anything, and that regulation was keeping them honest.
That was a bit off topic, but it all comes to together to show why non-Americans get upset by the remakes.