Giants fan here. It's really the fans that change my attitude towards teams. I respect rivalries. But it's dumb fans that get the hate.
1. Eagles. Their stab-happy, tough-talking fans deserve all the hate in the world. It's great to say, "NO SUPERBOWLS FOR YOU!" They use the bitterness of losing as an excuse to assualt children. Love that McNabb though. He doesn't deserve the crap being flung at him. Ironically, a few Eagles fans I spoken to are nice dudes and chicks. Too bad they get drowned out by the crassness of the many.
2. Commanders, since Joe Gibbs returned. It's like the Commanders are all of a sudden coached by God. And this God is whiny about the refs. As always there are those few who don't fit the bill. Also they have a big win over the Cowboys and the sports media has once again been acting like they are going to the Superbowl.
3. Cowboys. I'm apathetic towards you guys. I have no ill will. You're the least whiny of NFC East fans(Including my own). Your team is the gold standard in the Superbowl era. I think you guys have owned the Giants. But again, that reluctance to blame the refs is remarkable. Must be a Texas thing. Maybe if you had swept us, then I would have felt something. But otherwise, meh.
I can tell who Phoenix-Talon hates. I notice you're trying to drive these guys to hate the Giants as well. I don't think they will ever forgive the Eagles fans for cheering Michael Irvin's injury though. And of course there is the Commanders rivalry, so there's that "hate" between Cowyboys and Injuns. Both teams clashed for many years. They have both been dominant at the same time.
But the Giants have sucked when the Cowboys have been good. No chance to develop a rivalry or hate.