well by now we know about her pretty much a lot, and the reason everyone hates her is because of rumors about her from her previous school/academy whatever.
Sattelizer is: very feminine, disturbed and traumatized beautiful girl, during the carnival she can easily defeat any opponent simply because she doesn't want to be touched, that comes from her trauma from the past, as she seems to have been molested, very possible it was done by her first limiter, I deduce that from the flashbacks that show up and how she comments on him touching her. Most of the students just hate her for the sake of it, or simply because everyone else hates her and they don't want to stand out, they all just don't understand her, but I don't blame them fr it, she barely ever talks about herself. Hence i want to bitch clap everyone in that show except Sattelizer with a shovel.