I'd only look to animals for ideas of where rights come from if I saw no distinction between the humans and animals.

There is evidence that suggests humans are born with moral intuition. There is a natural aversion to killing others (that can be overcome by conditioning) which suggests there is at least one natural law. There is also research suggesting that human babies have a sense for fair play and justice. I'll have to cite this at some point; I believe I read it a Malcom Gladwell book.

You also still haven't explained how society decides what is desirable and what is not. If you keep asking why, it will eventually lead to a natural right or fundamental good.