Yesterday's post was kept to a strictly natural level, without regard to the dimension of man's relationship with God and the fact that the natural world and all it contains were created by God.
If animals have rights, it would only be because God endowed them with rights. The deer or cow or whatever, as such, does not appear to be a subject of rights. If God has conferred rights upon them, those rights would not be natural rights, but conferred. In contrast, man has been created to be a subject of natural rights. While I cannot necessarily point to any biological structure where rights reside, man's natural and normal ability to ponder and discuss rights, duties, ethics, justice, and so on, proves that to be human is to be a subject of rights.
A brief aside: It is not this ability that causes humans to have rights, no more than the light that fire emits causes it to be bright, because one could say it is because fire is by nature bright that causes it to emit light. Emitted light and brightness are simply different ways of looking at the same thing. The brightness of the fire proves that it emits light, just as our ability to discuss and act regarding rights proves we have rights. Therefore, if individual human beings lack this ability due to immaturity, disease, sleep, or some such thing, the disability is unnatural. In comparison, if animals lack of this ability because of the kind of thing they are, the inability is natural. It is not an unnatural "dis-ability" but a natural "in-ability." Earthworms are not blind (which implies the lack of a normal power); they simply cannot see. Given time to grow up or an effective medical treatment, a disabled human would (re)gain the natural human ability being discussed. Therefore, it is a fallacy to say that since some individual humans lack cognitive ability and yet are subjects of rights, other animals that lack that ability also have rights.
Now, if God has conferred rights upon animals, this would be an important thing for humans to consider and act on. However, there is no way for humans to know if God has done this or not through simple observation of the animals. There is no evidence in the behavior of animals that they are subjects of rights. They see, they smell, they feel, but rights are totally beyond their experience. The only way for us humans to know God has endowed animals with rights is if He reveals this fact to us. Such revelation is lacking, however.
It cannot be that animals have rights because God made animals. God also made rocks and the hydrogen that thinly permeates the far reaches of space. If all things have rights by virtue of having been made by God, then it cannot be that all things have equal rights. If a stone had equal rights to the rain, the rain would commit an injustice by wearing it down over time, or by penetrating its cracks and freezing in the winter to split it. Animals would commit an injustice to plants by eating them. Therefore, those things that are superior kinds of beings have greater rights than the inferior. So, living things have superior rights to non-living things, animals to plants, higher animals to lower (such as reptiles to insects, mammals to reptiles, dogs to rabbits). It stands to reason if we rank all created things in such a hierarchy, that one kind of thing rather than a group of different things would have superior rights over all. Since rights in this scheme come from having been made by God, it would stand to reason that the thing with the greatest rights would be the thing that God has made to be most like Himself. Since only humans have the capacity to even ponder this idea and to create, God being omniscient and omnipotent, humans clearly are the most God-like of known life forms. The rights of humans therefore supersede any rights animals might have by virtue of being made by God.
However, the fact that they are made by God does indicate that they belong to God in some way. As such, all of creation right down to the grains of sand on the seashore, should be respected by humans, and looked upon with awe and wonder. Two things need to be said about this. One is this: If we speak informally to say that rocks and trees and animals "deserve" respect, we speak only analogously. It is God Who deserves the respect we should extend to creation, and creation "deserves" it only by virtue of creation belonging to God, and our use of the word more indicates our duty, something in us, than something in creation. The other thing is this: Respect does not mean everything is sacrosanct and untouchable and unusable. If you borrow a book from me and respect the book the way it "deserves" (=the way you ought) because it is mine, that does not mean you do not read it. It means that when you do read it, you handle it carefully.
So, I do advocate the humane treatment of animals but do not advocate the notion that all human use of animals is inherently inhumane. Animals can be kept as pets, or raised to give eggs, milk, fur, leather, and meat, or hunted for food or to protect crops and livestock and people with no injustice done. It is not these things that are intrinsically unjust or disrespectful. It is how humans go about doing those sorts of things that determines whether or not it is disrespectful. Stewardship of God's creation precludes both abuse and neglect. Stewardship means using what God has made, but with respect for the fact that God made it.
And again, if animals have any rights at all, this notion of "rights" is only analogous. It speaks to our duty and points beyond the animals to God as the object of our duty and respect, rather than speaking to something in deer and rats as such that demands justice. It is an informal and colloquial way of speaking and not scientific or expository in a formal sense.