I could be way out of line here, but it seems to me that a living being only has the rights and/or self-ownership that it is 1) capable of recognizing, 2) capable of exercising, and 3) capable of enforcing.
Considering it from that perspective, I would say that yes, animals are self-owners (to some extent) and they do have rights.
Capability of recognition, I think, goes without saying. Animals are still alive, and they do not simply sit and resign themselves to death when a predator comes. This clearly demonstrates that animals are in clear recognition at least of a right to life. (It should be noted that predators - humans included and yes, humans are predators - have a right to live, too. This means that they also have the right to hunt other species to fulfill their need for food. It’s all a part of the balance of life, but that is just my opinion.)
As for exercising their rights, animals do it every day. Whether it is by self-aware recognition or instinct is irrelevent. Animals simply do the things that they, as self-owners, need to continue living.
And as for enforcing, that again is pretty clear. They flee, they fight, they do what they perceive - intelligently or instinctively - as necessary to survival. It’s what they do. Try hunting a boar without a boar spear or a high-power rifle and you’re probably in for it. You go at a wolf or a large cat with your bare hands, and I’m laying my bets on the wolf or the cat.
I would say that animals - no differently from humans - have rights, so to speak. However, I also think our society has grossly misrepresented and misinterpreted the entire concept of rights. As I said, a being only has rights they are willing and able to enforce. The earth is a predator-prey kind of place and the only solution available to human and animal alike is to attempt not to be prey.
The concepts of legal legal and natural rights are bunk. To have legal rights, you must place your self in the hands of a predator entity (government) in the hopes that it will benevolently protect your rights. Doing so, however, negates your self-ownership and by extension actually negates all of your rights, even those the predatory entity claims to protect. To quote a friend at school…the concept of legal rights “is grade-A horse hockey.” Governments do not and cannot protect your rights. The existence of rights is a self-made decision, and that decision includes enforcing them. Nobody can do it for you. You as a human being must stand up and assert them. As for natural rights, history and nature herself both beg strongly to differ with that concept. Where is the gazelle’s right to live when the lion catches it? Or the right to liberty of the deer surrounded by a pack of wolves? Or pursuit of happiness for the millions of animals that starve to death over harsh winters? They had none to begin with except those that they were prepared to assert, even over the objections of others. God (or nature or evolution, whatever) grants us - and animals - only self-ownership…the only real right which includes our ability to decide what our personal rights are and to assert them for ourselves. Personal opinion, concepts of legal and natural rights are both inherently dangerous as they often negate assertion and enforcement by individuals or species. Without assertion and enforcement, rights don’t exist.
Does the animal have a right to live? If it is willing to assert and enforce it, yes. However, so do humans, and like it or not humans are predators. Humans require meat to survive - red meat being the richest natural source of iron, animal fat and dairy being among the best sources of EFAs, and red meat being the only natural source of vitamin B12 (all according to the Centers for Disease Control and Prevention) - and (contrary to the beliefs pushed by animal rights activists and vegans) humans cannot survive on vegetable matter alone for prolonged periods of time. Now, unlike dedicated carnivores we are omnivorous predators, so we also do require a balance of meat and vegetable matter to survive. That, however, does not negate the inherent - and instinctive - predatory nature of humans as animals. In the predator-prey relationship that is life, humans must occasionally continue to live by violating the perceived right to live of the animal. Cold hard fact, sorry.
Perhaps, though, I am way out of line on all of that. That, though, is my current opinion on rights.
Now, taking it a step further into animal abuse:
So long as the animal recognizes you as an owner or leader - “boss” cat, alpha dog, whatever - then you, frankly, can do whatever you want to it. That’s how the pack and the pride work. “Boss” cat and alpha dog get the first pickins, and everyone else gets the scraps. If there’s a disagreement, they fight and might makes right. That’s just how it works, I see it all the time with my two cats. However, there may come a time when a dog perceives weakness or a cat decides to fight back. Again, might makes right as far as the animal is concerned.
If a person wants to abuse their animal(s), more power to them, if that’s how they get their jollies. But if they get bit, mauled, clawed, or killed by the animal they’re abusing, I’ll then assert my right to cheer the animal on. Again, life is predator-prey and if the animal decides not to be prey, well then we have a problem, don’t we? We now have a conflict of predators deciding who is prey. As far as an animal is concerned, might makes right, and the animal is going to be quite certain that he’s the right one. When a human being asserts his or her right(s) over an animal, they can do so only so long as they are prepared to reap the consequences of failure.
Again, perhaps I’m way out of line on that, but that’s just how I’m perceiving things right now.