Argument: Animals cannot make moral claims so cannot claim rights
Carl Cohen. "Why animals have no rights. The Case for the Use of Animals in Biomedical Research" The New England Journal of Medicine 315, no. 14 (October 2,1986): 865-69 - "The differing targets, contents, and sources of rights, and their inevitable conflict, together weave a tangled web. Notwithstanding all such complications, this much is clear about rights in general: they are in every case claims, or potential claims, within a community of moral agents. Rights arise, and can be intelligibly defended, only among beings who actually do, or can, make moral claims against one another. Whatever else rights may be, therefore, they are necessarily human; their possessors are persons, human beings.
The attributes of human beings from which this moral capability arises have been described variously by philosophers, both ancient and modern: the inner consciousness of a free will (Saint Augustine); the grasp, by human reason, of the binding character of moral law (Saint Thomas); the self-conscious participation of human beings in an objective ethical order (Hegel); human membership in an organic moral community (Bradley); the development of the human self through the consciousness of other moral selves (Mead); and the underivative, intuitive cognition of the rightness of an action (Prichard). Most influential has been Immanuel Kant's emphasis on the universal human possession of a uniquely moral will and the autonomy its use entails. Humans confront choices that are purely moral; humans -- but certainly not dogs or mice -- lay down moral laws, for others and for themselves. Human beings are self-legislative, morally auto-nomous [sic]. [p.865-866]
Animals (that is, nonhuman animals, the ordinary sense of that word) lack this capacity for free moral judgment. They are not beings of a kind capable of exercising or responding to moral claims. Animals therefore have no rights, and they can have none. This is the core of the argument about the alleged rights of animals. The holders of rights must have the capacity to comprehend rules of duty, governing all including themselves. In applying such rules, the holders of rights must recognize possible conflicts between what is in their own interest and what is just. Only in a community of beings capable of self-restricting moral judgments can the concept of a right be correctly invoked."
Constant. "No rights for animals". The Distributed Republic. June 21st, 2007 - "what gives human law bite is not that an individual will defend himself (all animals defend themselves), but that where there is a conflict, humans all around will decide who's right and side with the one in the right. This happens all the time though nowadays it's largely taken over by the state and its police, who jealously guard their privilege to identify and team up against malefactors. Vigilantes not welcome wherever a state holds sway. But it's essentially the same as in anarchy: where there is a conflict, the good guy (if there is one) and bad guy are identified and essentially all of society goes after the bad guy (be it directly through vigilantism or mediated by a government with its police force).
Animals can't do this, or at least, their ability to do this is strictly limited. If you murder a human and are seen doing it, then your description can be spread far and wide and you will not be entirely safe in human society anywhere. But go up to a dog, even in plain view of other dogs, and kill it, and you are safe, in large part because dogs have no ability to spread information about your actions. If dogs had that ability, then things might be different. But they don't. And same with cats, horses, birds, snakes, whatever. You can predate on non-human animals openly without fear of "animal society" turning on you. You can't do that with humans."