Since I was a child I was used to having pets in my home or in my garden. Usually cats, but later when I grew up I had the chance to posess sheep, horses, dog, birds and other animals as well.
I have devoted a lot of my intuition and understanding into communicating and learning animal behaviour and that has added a lot of experience for me.
Not all animal races are identical. Certain types of birds have their particular ways of herding and comunication, felidae like sparse herding and have brutal social rules, dogs among canids have a strong coherence and integrity with human communication so that they abolish their canine social structure. Horses have a strong intellectual entity and pride but they abide to the human rule which can provide them safety from predators and uncontrollable herd expansion in expense of their pride and herding rules.
Some people host rodents as pets and I've seen that even rodents develop remarkable skills of communication, obedience and coherence to their lord's lifestyle.
And all that I say in order to justify that to me most animals, even reptiles and fish, possess the potential of domestication and communication with humans. To me most animals could become pets.