If you're arguing against zoos, the approach I'd take is referencing Darwinism with respect to humans and animals having common ancestry. And then you could say, since we have a common ancestor, it follows that we're entitled to many of the same basic rights, and we don't believe in doing this to people.
Personally, I think the Pro-Zoo viewpoint has a lot going for it, and there's where I stand as well, but if you're arguing against zoos I think the best thing you can do is stick to blurring the line between people and animals. That will make a strong case.