Why did Izumo's familiars attack her in Blue Exorcist?
Familiars in the manga are actually tamed demons. If the user is not properly trained in controlling them or have a disturbed state of mind then the go out of control. Before Izumo was attacked by ghouls, Paku said she was going to quit the course. Hence she was in a disturbed state of mind. So the familiars attacked her.
According to wiki about her foxes


  White Foxes appear to be very proud, even willing to turn against those they've been raised with if they sense weakness.