“Why are you in this war?”
“For me rats!”
“I think he means: his rights.”
“Oh… Never could understand anyone south of Maryland.”
— Gettysburg, 1993
The main idea is: humans have equal rights with other humans; animals don’t, because they are, well, not humans. Otherwise, their rights would have to be protected against each other — if I cannot kill a cow to eat it, neither can a wolf.
Some people answer that a wolf cannot be judged for following his nature; he does not have a choice about eating a cow. If by that they mean that he cannot make a rational choice — well, that is exactly the point! To have rights apply to you, you need to be a moral subject which requires rationality. (What about children and mentally ill? The articles addresses that too.) If by not having a choice they mean that the wolf is a carnivore — what if people were carnivores? Would animals magically lose their rights? What if someone cannot digest fruits and vegetables or simply needs meat for medical reasons (otherwise, he cannot survive) — do animals lose their rights regarding him, but not others?
The author agrees that animal cruelty “does not belong in any civilized society”, but doesn’t propose how to deal with it (if at all) — I think it is outside the scope of this article.
The idea of rights is a peculiar one. Where do humans get their rights? Three arguments can be made: from their Creator, from the Nature, from pragmatic convention included in the agreement to live together in a society (if I am going to live in a society with you, I am going to have certain liberties — the same as you or anyone else — that cannot be violated; the only time my liberty to do X can be violated is when it is violating another person’s liberty to do Y, which is considered by the society as more important).
Following the “Creator” argument: well, my religion says nothing about animals having rights. One cannot treat animals cruelly and must ease a struggling donkey’s burden (in fact, even your enemy’s donkey’s burden!), but eating animals is not forbidden — in some cases it’s even required. If your religion says otherwise, you’ll have to prove to me that your religion makes more sense than mine (considering that mine is Judaism, I find that unlikely).
I don’t think the “Nature” argument can be made cohesively: I am yet to be shown how exactly our rights derive from Nature — but even if they did so from our special status as sentient beings in the Nature, animals would lack them precisely because of their different nature from ours (which, I think, is the main focus of the article). If a rational species were to be discovered (or existed alongside with humans — e.g., elves, dwarves, hobbits), I don’t think anyone would argue that eating its members is wrong (although we probably would have to deal with some racism...).
Finally, the pragmatic argument simply has no place for animals in it: human rights exist within the scope of the society to which these humans belong. Animals are not a part of our society.