I've tried to tackle the thorny issue of where rights come from in some of my research work, and I reproduce that part of the work below with minor updates and new references.
However, let's begin by reminding ourselves that Professor Tom Regan, the author of The Case for Animal Rights, grounds the notion of animal rights in the tradition of "natural rights"...
Rights and Animal Rights.
Tom Regan and Gary Francione are acknowledged as the major theoreticians of perspectives that seek to build on established rights formulations, and apply - or extent - to them to nonhuman animals. Regan is a Kantian deontologist who argues that many nonhumans are "subjects-of-a-life," a factor demanding that humans respect their inherent rights. Francione is a law professor particularly critical of the property status of other animals. His rights-based formulation is thought less complicated than Regan’s; he claims basic rights for all sentient beings.
Reganite and Francionian positions on nonhuman-human relations can be regarded as attempts to bring genuine rights views to bear on the issue of the human use of other animals. Such approaches are different in nature to traditional or classical welfarist stances; and different also from Peter Singer’s version of utilitarianism which...Francione claims as the philosophical grounding of modern day "new welfarism." Neither Regan nor Francione use rights concepts, or the language of rights, in a rhetorical manner as many other animal activists do, and both believe that protective rights formulations can be plausibly extended to prevent current large-scale institutionalised human exploitation of certain species of other animals. Regan’s and particularly Francione’s works are effectively marginalised even within the animal advocacy movement. This section, therefore, acknowledges and highlights a paradoxical situation in which the so-called "animal rights movement" virtually rejects genuine rights theories while embracing a non-rights animal liberation position as its main philosophical stance.
As implied above, however, it may be recognised that even the phrase "philosophical stance" can be quite misleading in relation to the majority of current animal advocacy in which "philosophising" per se is actively frowned upon, and/or seen as a very poor second to "doing things" (doing any thing) "for the animals." The modern animal protection movement, as well as its counter-movement mobilisations, frequently (and correctly) presents the book Animal Liberation as the origins of second wave nonhuman advocacy, along with an implicit and often explicit (and incorrect) claim that the book, and therefore the movement, is based on Peter Singer’s "animal rights perspective."
The frequent characterisation of his utilitarian perspective as an animal rights position, and presumably the number of times Animal Liberation has been described as "the animal rights bible," has seemingly led its author to regret ever having used rights language, even rhetorically and, according to Regan (2001: 83-4), Singer remains committed to his claim that attributing rights to nonhumans is not possible.
[...] some of the misrepresentation of Singer’s work as rights-based theorising, especially by pro-use countermovements, appears on the face of it to be deliberately ideological in intent. However, in relation to what Singer says about his own position, Francione fully accepts that Singer is entirely consistent to the extent that he rejects the notion of moral right holding in the case of human and nonhuman animals. Moreover, his consistent utilitarian principles have led Singer to accept that "there might be circumstances" in which human and animal exploitation…could be justified in light of consequences (Francione 1995: 259).
Francione suggests, however, that rights concepts are always likely to be important and invoked as resources in human affairs and therefore utilitarian "balancing" of human and nonhuman interests are extremely dangerous in terms of nonhuman interests. Dangerous precisely because protective rights considerations are not conceptually available "to limit the results of the balancing process" (ibid.) Francione attempts to clarify the point by putting it in a different way, while at the same time revealing how authentic animal rights theorists attempt to build on already established ways of thinking about the protection afforded by bearing rights:
the utilitarian notion of “consequences” cannot be interpreted in a way that does not prejudice the issue of animal protection. Even if we do accept that animals have interests, it is simply difficult to make determinations of those interests from a humanocentric perspective; it is because we systematically devalue and underestimate the interests of disempowered populations that rights concepts are necessary in the first place. Although rights theory rests ultimately upon a consideration of animal interests, rights theory does not permit the sacrifice of animal interests simply because human interests would be served. Rather, rights theory assumes that at least some animal interests are entitled to prima facie protection and that the sacrifice of those interests require a justification not dissimilar to that required when we seek to override human interests protected by rights (ibid.)
Kangas suggests that the understanding of the first question of where rights "come from" can be aided by separating out three types of thinking about rights: conservative, liberal and libertarian; and also by thinking about four initial bases put forward for the creation of rights: that rights are "natural" (following Locke), "inalienable," "God-given," and "self-evident." Kangas states that until a few hundred years ago, most philosophers believed that rights could be defined in these four ways. However, "today, most philosophers agree that rights are social constructs, open to change." He says that this view accords well with the "liberal" stance, since, "Liberals believe that rights are social constructions, defended by force and open to change and improvement."
Kangas is almost certainly correct to state that rights cannot be regarded as self-evident because, as he notes, "philosophers have been vigorously arguing about them for thousands of years" (ibid.) Kangas also finds support in his assertion that debates about rights can be messy and complex. For example, Carl Cohen, in his 1986 article, "Why Animals Have No Rights," [the original is again broken, so THIS replaces it] states that, "The differing targets, contents, and sources of rights, and their inevitable conflict, together weave a tangled web." Cohen’s title itself indicates philosophical controversy over recent rights claims. He has published a number of works addressing human rights concepts and the whole idea of nonhumans being right holders. Whereas theorists such as Cohen argue that nonhuman animals, as a matter of logic, cannot ever be said to bear rights, Regan and Francione disagree and have put forward differing ways by which they argue that rights formulations can and should protect sentient nonhuman interests. While Regan’s position has been described as a liberal rights perspective (Fiddes 1991: 196), Regan characterise Cohen, like Singer, as a utilitarian theorist, at least "when reasoning in support of continued widespread and possible expanded reliance on nonhuman animals in biomedical research" (Regan 2001: 70). The difference between Cohen and Singer is that Singer argues that no animal, human or nonhuman, can hold rights, while Cohen argues that all humans do and nonhumans do not.
Regan claims to adhere seriously to a commitment to develop an "informed, thoughtful moral outlook" (2001: 101). According to Benton & Redfearn, strength within Regan’s strategy accrues from the "benefit of latching on to the currently near-universal moral priority attached to human rights" (1996: 51, emphasis in original). Although it may be rather unkind of them to label Regan’s approach "a strategy," as if his commitment to human rights was only for the following reason, Benton & Redfearn acknowledge that, "Regan was the first theorist to get 'rights' across the species barrier" (ibid.: 50). Therefore, Regan can be credited with breaching that hitherto solid defensive ethical barrier based exclusively on species membership, of which the construction, maintenance, and usage of featured prominently in Part One of the current work.
Benton & Redfearn state that, as a matter of historical record, "the ethics of the 'rights' tradition has been markedly anthropocentric. To 'qualify' as an inherently valuable being one had to possess 'reason,' 'autonomy,' 'moral agency' or some other capacity generally restricted to humans" (ibid.) Regan, they go on, gets morality over the species barrier by concentrating on the criteria of right holding, a familiar notion in rights discourse addressing the question of the expansion of rights bearing. Clearly, many human beings do not have the characteristics listed by Benton & Redfearn above, neither do many have language use, another favoured way of deciding who holds rights. There is therefore a philosophical puzzle to be solved here. Either human beings without the above capacities are themselves not right holders or, if they remain so, on what basis are nonhumans, with similar capacities, to be denied at least basic or negative rights?
In general rights discourse, the notion that rights have been converted from shields to swords is seriously contested by various theorists: however, in this formulation, the idea of animal rights is clearly about rights as protective shields for individuals. Regan’s "subjects-of-a-life" are not necessarily moral agents; and logically nonhuman animals are placed into the category of right holding moral patients along with certain "marginal" humans (as they have became known in rights discourse) (DeGrazia 1996). Using a post-Darwinian understanding of the psychological complexity of many nonhumans, Benton & Redfearn claim that Regan shows that, "though animals are not moral agents in the full sense, they have enough sense of self as persisting through time, ability to express preferences and so on to be said to have 'interests,' which may be harmed or favoured by human agents" (1996: 50) Benton & Redfearn investigate the "lesser-than" aspect of "moral marginals," and conclude that not only are they not denied protective rights, "On the contrary, it might well be argued that it is just because of their lack of these attributes that they are in special need of the protection offered by the attribution of rights" (ibid.: 50-1).
For these commentators, Regan’s concentration on the rights of the individual strengthens the rights approach over what they describe as the more moderate "linkage of utilitarianism and animal welfare reform" (ibid.: 51). The one advantage of utilitarianism, they claim, is its reliance on "mere sentience" as the ethically relevant criteria. The strength of that, they say, is due to the fact that hardly anyone in the modern world would dispute that many nonhumans are sentient beings. A further "strategic limitation" of Regan’s position, Benton & Redfearn argue, stems from the huge social and personal changes implied by respect for the rights of many nonhuman animals. This would require, "both social transformation and lifestyle changes of very fundamental kinds." How many, they ask, will be prepared to adopt a vegan diet and avoid all animal products? Surely, only those who could adhere to veganism can remain consistent with the logic of animal rights? This question greatly interests animal advocates, many of whom suggest that a strict advocacy of the vegan diet can be "divisive" and "elitist," whereas others simply see it as a logical consequence of accepting the rights view about human-nonhuman relations (Francione 1996: 43-44, 239).
Francione’s position is free of the first "limitation" in Regan – but clearly not of the second. In other words, Francione’s basic right theory argues that a being’s sentiency alone is enough to demand that humans respect their rights. Francione also firmly declares that respect for nonhuman rights does indeed require the personal adoption of veganism as a lifestyle choice. Francione begins his outline of animal rights with a familiar warning common in accounts of rights discourse: "There is a great deal of confusion surrounding the concept of rights" (2000: xxvi). His focus is on one aspect of rights, the protection they may offer, and argues that this is common feature of virtually every theory about rights: in other words, "a right is a particular way of protecting interests":
To say that an interest is protected by a right is to say that the interest is protected against being ignored or violated simply because this will benefit someone else. We can think of a right of any sort as a fence or a wall that surrounds an interest and upon which hangs a “no trespass” sign that forbids entry, even if it would be beneficial to the person seeking that entry (ibid.)
Moving toward his conception of animal rights, while accepting that no rights are absolute, "in the sense that their protection has no exception" (ibid.: xxvii), Francione builds on the notion that all humans "who are not brain dead or otherwise nonsentient" (and presumably who are not masochistic) have an interest in avoiding suffering and pain (ibid.) This interest is tied to the importance of being a legal person:
Although we do not protect humans from all suffering, and although we may not even agree about which human interests should be protected by rights, we generally agree that all humans should be protected from suffering that results from being used as the property or commodity of another human…in a world deeply divided on many moral issues, one of the few norms endorsed by the international community is the prohibition of human slavery. Nor is it a matter of whether the particular form of slavery is “humane” or not; we condemn all human slavery (ibid.)
If we apply the principle of equal consideration to animals, then we must extend to animals the one basic right that we extent to all human beings: the basic right not to be treated as things (ibid.: xxix).
 Throughout Animal Liberation Professor Singer is careful to talk about the "Animal Liberation movement" and never speaks of a clash between human and nonhuman rights, rather human and animal interests. In the 2nd edition ofAnimal Liberation, Singer was motivated to say something about rights formulations: "The language of rights is a convenient political shorthand. It is even more valuable in the era of thirty-second TVA news clips" (Singer 1990, cited by Francione 1996: 49, 240).
 If Kangas is correct that talking about the origins of rights is messy, the same may be said of the claimed position adopted by this or that theorist. For example, while Regan suggests that Cohen takes a utilitarian line, Nathan Nobis (2002, in a review of Cohen and Regan) states that, "Cohen and Regan give high regard to moral rights… Both are decidedly anti-utilitarian."
 Benton & Redfearn (1996) also note that Regan’s rights approach will find opposition in some perspectives based on "ecological morality." For example, the rights view implies that only animals that resemble humans in relevant ways "qualify" as right bearers. Animal rights theory, they note, "offers nothing at all to animals not conforming to the 'subject of a life' criterion" (1996: 51).
Benton, T. & Redfearn, S. (1996) ‘The Politics of Animal Rights - Where is the Left?’ New Left Review, Jan/Feb: 43-58.
DeGrazia, D. (1996) Taking Animals Seriously: Mental life and moral status. Cambridge: Cambridge University Press.
Fiddes, N. (1991) Meat: A natural symbol. London: Routledge.
Francione, G.L. (1995) Animals, Property, and the Law. Philadelphia: Temple University Press.
Francione, G. L. (1996) ‘Ecofeminism and Animal Rights’ - a book review and commentary - review of “Beyond Animal Rights: A feminist caring ethic for the treatment of animals”, edited by C. Adams & J. Donovan’, Women’s Rights Law Reporter, Fall (email version supplied by Lee Hall in April 2002).
Francione, G.L. (2000) Introduction to Animal Rights: Your child or the dog? Philadelphia: Temple University Press.
Nobis, N. (2002) ‘Review of Carl Cohen & Tom Regan’s The Animal Rights Debate (2001), Jornal of Value Inquiry, Vol 36(4): 579-83.
Regan, T. (2001) Defending Animal Rights. Urbana & Chicago: University of Illinois Press.