Some guy will post a picture of a pretty standard looking pepperoni pizza and say: "Imagine not living in new york." And then there's the whole bodega discourse, which is also funny. "For you non-new yorkers, let me explain: a bodega is not a corner store. It's a place where you can buy gatorade, toilet paper, AND eggs." Thank you sir for explaining that to a slack-jawed yokel such as myself.
That's part of it, but I would say more than anything it is because NY is itself pretty pampered and important, so shitting on it is fun. Plenty of people who live in smaller, but still huge cities hate New York as much as anyone. What's the point of living in a city if you dont hate everything about all other cities, and also hate your own city too?