Chikako is probably bullied because her family has an inugami. Considering that it's out in the open, I wonder if the setting is a school for supernatural beings? Or is Inukami invisible to humans and Taki's identity is a secret?
You wouls think using the inugami to gently and non-permananently harm the bullies to keep them away would make sense, but she wants that catgirl's attention dammit.