Maybe i'm just being to literal about this, but i've always wondered why we have been able to have pets that are like other humans. I'm fine with having a dragon, blood bat, or fire cat be called a pet, but why are we able to have pet Seraphs, Judgements, Satyrs, Cyclops? Even things such as helephants, krakens, and minotaurs seem more humanoid than animal.
Maybe instead of calling them pets, calling them companions, since that would fit everything?
I would suggest the term "familiar" but i'm sure that would rally the fanatics, but it would be more in keeping with the witch and wizard lore/theme, as familiars provided certain abilities and assist their master with a variety of tasks.