My Dad grew up on a farm. My grandpa raised chickens and hogs and crops. One time when one of their sows had a litter there was a runt in the group. Most of the time runts were euthanized as they rarely survived on their own. This time, for some reason, Grandpa kept the runt and took it into the house where they kept it warm and bottle fed it until it was stronger. After caring for it and saving it's life the family became kind of bonded to this little pig so they named it Orville and kept it as a pet. Orville had the run of the farm and played with my Dad and hung out around the family and their other pets. Orville prefered the company of people over other pigs. Orville lived to a ripe old age with a loving family while his brothers and sisters were slaughtered, butchered, smoked and eaten while still young.
I guess my point to this is that we as individuals decide what is and what is not a pet, it is NOT dependent on species but how we as people interact with a particular animal. Pets are not born, pets are created by how we feel and become emotionally attached to an individual animal.