The party line is that animals have a right to live free of human interference. I'm not giving them the "free of human interference" part for several reasons. One is because if it is a moral principle, then moral principles come from the alleged minds of people who have anti-social personality disorder because their "reasoning" comes from a hatred of their own species.
The human species is the first species that has shown a desire or an ability to be less destructive to its own environment. This destruction is a normal product of use. Herbivores use the environment and if predation and disease didn't stop them they would eat all of the greenery and starve and die. Even the greenery would choke itself off and die if it didn't have the herbivores and fire to kill some of it off once in a while. An intelligent species can control this process with less waste, less disease, and can ensure the future of other species. One of the best things that we have done is transplant other species around the planet, thus increasing the geographical spread of unique genomes.
I can't say that a species has a right to what it needs as long as it doesn't interfere with the rights of others. Other life competes with and fights with each other. Humans have at least as much right as other animals to be a part of this. There are other examples of different species that cooperate with each other but humans are the one species that seems to be willing and able to work cooperatively with a very wide variety of non-human species. We are also the one species that is willing and able to work on behalf of that wide variety of species.
Were there such a thing as an animal rights activist, that activist would be for the most essential rights of an animal. These would be the right to exist and the right to propagate. They would be for legislation that forced humans to take in as many animals as possible, and considering how loosely connected to reality the "animal rights" activist is, "possible" takes on a whole new meaning. It's kind of a relief because I might find out that I only want one or two big cats, not the whole hoard that keeps getting thrust on big cat enthusiasts.
It's not just PETA killing animals or the HSUS with its killing vans and swindling judges into ordering the deaths of pitbull pups. It's a determined effort to stop private breeding and to get as many non-humans dead or under their control as they can. Preventing births looks a little like saving lives, but it works like euthanasia in advance. When one to three percent of the pet population ends up being killed as "overpopulation" then for every pet saved from that experience, at least thirty-three births have to be prevented. That's a dead loss. If we looked at it from a viewpoint that permitted joy, we would take pleasure in the fact that very few pets die that way.
PETA, the HSUS, and the growing cottage industry of swindlers, self-haters, and terrorists don't care about the animals. They just care about money and the pain that they can cause humans and animals.