students. She is revealed to be intensely bigoted , harbouring deep loathing for "half-breeds", such as centaurs , werewolves , and Rubeus Hagrid (a half- giant ). She dismisses Sybill Trelawney , the Divination teacher, as incompetent, places Hagrid on probation, and bans Harry, Fred and George Weasley from the Gryffindor