That depends on what you mean by the term "pet." When I hear the word pet, I think of dogs, cats, fish, rabbits, the occasional gecko, guinea pigs, maybe a ferret or two. Those are animals that, at least within their breed, have been domesticated to a certain degree. A guinea pig would never survive in the wild!
However, it is true that these animals are sometimes mistreated. That most definitely goes against their rights.
There are also times that your lifestyle can affect your pet. For example, let's say that you own a fish. You also so happen to live in an apartment. Fish don't need to be walked or to have fresh air. They are fine in an apartment. Now, suppose the fish dies. Sad, I know. You are also sad, so you decide to get a dog (it lives longer, after all.) to replace it. Your dog needs fresh air, walks, and a proper bathroom are. So, you set on grass on your patio and arrange with your mom to walk the dog at least twice a day and take it to the dog park a couple times a week. This situation could possibly work, as long as the dog gets everything that it needs. Ideally, it needs a yard, but you are making sure that it gets enough exercise. The dog is probably not the happiest animal right now. You might need to consider a new pet, since the dog is not enjoying life to its fullest. Then, you make a major mistake. You pick a full-grown horse as your next pet. This situation is totally unacceptable, as the horse is being kept in a stable far from where you live and is therefore getting little companionship and probably not enough exercise. You aren't in the right circumstances to own this pet. Which brings me to my next point...
Crossing the line. I do not care for exotic pets. Personally, I hate the thought of a bird in a cage in the first place, but what if you bought a parrot or a peacock, you know, an animal that is used to living in the wild. That is an infringement on animal rights. You have taken the non-domesticated animal and personally captured it. There are all kinds of pets that experience this, though that normally occurs in the circus, or maybe a zoo, although they are supposedly helping the animals. That is crossing the line and is most definitely wrong.