Somehow, I don't think shammash and I will ever take that turn in our relationship to each other. I think we're going to stay in the human/familiar roles, and that'll be fine with both of us.
Speaking of which, the whole "parent of pets" thing is sort of weird. I can see how having a dependant animal puts one in a quasi-parental role, with the making of decisions, the care and feeding, and so forth, but pets don't exactly grow up and leave home, unless you're a rehabilitator, in which case they're more clients than they are pets. (What do rehabilitators call the animals they work with, anyway? Is there a specialized term?) And if you raise an animal from its childhood, you are in more of a parental role, but many of the people I notice using the parental terms to refer to their relationship with the critters may not have done this.
But you don't tend to have to nag a pet to clean its room or do its homework, just to stop barking and/or get off the damn counter already, as you're shedding on the toaster. (shammash sits on the toaster, the daft cat.)