Even though I'm not a big fan of animal experimentation or even the way people cook shellfish, the concept of applying "rights," a concept exclusively reserved for humans (by virtue of being created by humans) is an outgrowth of a childish anthropomorphizing of all that is "Cute and Fuzzy."
What "rights" do animals in the wild enjoy? The only rights that might bestows upon them. The strongest eat first, mate first (and most often), and receive the best of whatever the pack or tribal unit has.
The concept of "rights" as we understand them today is a strictly human invention. We started out similarly to the animals, giving fealty to the "alpha male" of our group, but when enough of us lower-echelon types got sick of getting seconds, thirds, or nothing at all, we banded together and invented rights. Look at how the Magna Charta was formed: lower-ranking citizens working together to force the ruling class to endorse their idea. Civil rights? Same thing: the underprivileged got together and worked to make sure they got their fair share. Think Hammurabi just decided to be a nice guy? No.
The same situation exists today. Take your "rights" as an American citizen to Zimbabwe and see if they're recognized. Try Iran or China if that doesn't work out. Or get out into the animal kingdom and try to assert yourself in an ape tribe using your human-given rights. Tell the alpha male just how wrong he is to take from you and explain to him the virtues of sharing and the concept of rights. Maybe there will be enough left of you to scrape up and put in a coffin. Despite the alleged complexities of primate languages and social customs, there is no way to communicate such an abstract concept as rights. That may be due to a lack of linguistic aptitude, or more likely they cannot communicate such a thought because they do not have such thoughts.
To apply the concepts of human rights to non-humans is a childish fallacy. Animals, although possessed of emotions and limited reasoning, are not human. "Human" is a term used to encompass all the traits--both virtues and vices--that make us human. From reasoning and rationality to temper and lusts, the sum total of these traits define human beings. Despite having some of these traits in common with us, animals do not possess them all and are thus not human.
As a simple example, a Camaro does not share all its traits with a Mustang. Despite common features--engine, doors, paint, etc.--they are not the same thing and are instead grouped under the general category of "cars," as we are lumped in with other animals under the general heading of "animals."
I tend to lean toward other posters' assertions that we, as the dominant life form on the planet, are in a position of custodianship over the lesser orders. And why not? We place ourselves in such positions over humans who are less able to care for themselves, such as our elderly citizens, our children, or those with lessened emotional or intellectual capacity. As the "ruling class" of animals that uses lower orders to further its own ends, it behooves us to make sure that they are "used" responsibly and are looked after with compassion and respect not because animals are cute and fluffy or are "people with fur," but because it is simply the right and proper thing to do, in itself a distinction that sets humans apart from animals, and a trait that animals do not and cannot possess.