It is morally normative to conclude that owning a pet dog is good because respectable, likable and powerful people such as doctors and first ladies do it, and as a consequence of it you can reduce stress, get exercise and stay healthy, form beneficial social bonds with other pet owners at the park, pet store and walking around your neighborhood.
It is also morally normative to think that owning a pet cow is not good because respectable, likable and powerful people don’t do that, there are city and neighborhood rules against it, a cow needs a lot of space and pet cows are not used for dairy, meat or leather and treating a cow like a pet is imprudent because it makes meat eating pet lovers uncomfortable.
Even if we change the word “owner” to “companion animal,” would it be morally defensible for beings with the power to do so, to separate us from our families and our natural environment, breed and obedience train us so that we are subservient, put leashes round our necks and use us for their health, companionship and social gain?
Every sentient being wants to be free, even domesticated dogs. If that weren’t the case and the breeding had truly taken all the “wild” out of them, we would not need all that obedience training, potty training, leashes or see so many signs for missing pets and hear so much barking from the dog who has been left alone all day in the neighbors back yard. If everybody does something, that does not make it good or right or just for you to do it. If it is your duty to do something that does not mean you should do it if it is unjust or unfair.
Common virtue ethics objection: “I am being compassionate by rescuing him/her from a pound or shelter”.
The problem with this line of reasoning is that when we rescue animals that are not normally pets, we take them to an animal sanctuary, where they can live out their lives in freedom with their own species. By making that rescue dog a new member of the family you are perpetuating a morally inconsistent distinction between “companion animals”, and animals who deserve to be free or to be ridden, or eaten, or experimented on. After rescuing someone from years in a prison camp we re-introduce them to free human society, even if it takes decades to do so and even if they never fully adjust.
I do see the apparent absurdity of making a sanctuary for Chihuahuas but, even with all their breeding, only a very few prefer human companionship to being with their own kind. So, why should some animals who have been trained and often bred to be in circuses and as “exotic” pets or lived for generations in cramped zoos be reintroduced to their natural habitat while others are not?