Gaga is hated because she is a threat to most of her peers on the charts right now whether fans of other artists want to admit it or not. In terms of albums, singles, tours, public recognition, etc., she's the biggest all-around pop star of her generation pretty easily. Everyone in the world not only knows the name Lady Gaga, but nearly everyone knows exactly who she is and has heard at least one or two songs by her. She's had the most impact on pop culture by any woman - really, any solo artist - since Britney Spears and possibly even further back than that. On top of her enormous commercial success, she also enjoys critical acclaim that many of her peers don't, has been heralded by many legends and icons who came before her, and is a multi-Grammy Award winner.
Monsters are hated on by association. Other stans can try to say it's because we brag, but so do others. It's stan culture. Bragging is what all of us do.