I think part of it is that they're so used to having to defend DS9 to fans of other series that they've taken to attaching unnecessary hyperbole to their arguments. They're in the mental habit of thinking they're talking to somebody who hates DS9 for equally stupid reasons like "It's not on a ship!"
But really I think TNG and DS9 are more similar to each other than any other two shows. Though DS9 showed more character conflict, the two shows had basically the same ideals and the same story resolution styles. I can't imagine how somebody could love one and hate the other unless they're applying some kind of extreme aesthetic bias.
Then there's the college kids who took economics 101, came to the conclusion that all altruism and optimism was evil and stupid and called it 'Libertarianism', then denigrate TNG on half-understood principle to prove how much smarter they are than everyone.