The term flyover country is stupid, but the people who use it probably wouldn't like living in places they call flyover country anyway. Just like living in Manhattan wouldn't be for me.
I personally like the term, though it does seem like a word that coast-dwellers use because they think the people of the Plains, Mountains, and anywhere they don't live are ignorant yokels. I respect every state in the union. I like the term, just because it sounds kind of modern and cool, but I can see why some people don't like it. I don't use it, because, despite the fact that I like it, it's not particularly specific and not really applicable to most situations.