If humans didn't exist, would animals still have rights?

We might start by pointing out that there's a controversy about just what rights are and also about whether animals have rights, but let's try to finesse those issues. On one common way of understanding rights, for me to have a right is for people or institutions to be obliged to treat me in a certain way. Whether that's the whole story, it's plausibly at least part of it. But cats, dogs and so on aren't obliged to act in any way; creatures who aren't capable of understanding obligations can't have any obligations.

If we put these two bits together, we get a plausible answer to your question: if there were no humans, then there wouldn't be anyone who had any obligations. (Of course, if there are non-humans who have the right kinds of minds, the story is different.) If there aren't any creatures who could have obligations, then the animals don't have rights.

We can back off this a bit. Let's use the term moral agent for any creature who is of the sort that can have moral obligations. Then even if there weren't any moral agents, it could still be that animals have what we might call "hypothetical rights": if there were any moral agents, they would be obliged to treat the animals in certain ways. But the idea that animals might have rights apart from any questions of how moral agents would be obliged to treat them is hard to fathom.

Read another response by Allen Stairs
Read another response about Animals, Ethics