To hate that which demeans us is probably an innate human tendency.
If people in the Islamic world feel demeaned by their relationship to the "bigger" world "on the other side of the screen," it may therefore be only natural for them to hate that world.
Unfortunately for us, to many people around the world, America and the "world on the other side of the screen" appear to be coequal. Thus, if America is the source of the images in whose magical presence people end up feeling small and dull and insignificant, it can feel only too natural for them to end up hating America.
It's hard to completely blame them for feeling this way. After all, the pictures they see do, for the most part, represent America.
But it would obviously be better if we could get them to see the difference between our real country and the wash of images they see on their screens.
How can we do this, though, unless we ourselves are sure of the difference?