When I came to New York 10 years ago, there were several beliefs I held constantly prior to becoming a "New Yorker":
1. Root for the home team.
2. If the home team doesn't make it, root for the division team.
3. If the division team doesn't make it, root for the league/conference team.
Then came New York.
The real Mets fans (those with passion) hate the Yankees and the real Yankees fans (those with passion) hate the Mets. Same for the Jets and Giants. Jets fans are usually Mets fans and Yankees fans are usually Giants fans. Any other combinations and you are a dysfunctional fan. In New York, there is no home team, only my team.
This is the difference between a city with one team in one league versus multiple teams in one league. This is the difference between a city that is big enough to be five cities (i.e. five boroughs) in one city versus just one city.
Admittedly, I miss the non-New York feel. This is why I have held on to my teams in Ohio outside of New York (Ohio is where I come from). More than one city in the same sport and league in one state is ok, but only in New York can more than one team fuel the torment of a minature nation known as New York City.