The question: Why animals don't have rights?

Rights are coextensive at the faculty of reason. To respect someone's rights means to treat him by persuasion, rather than by coercion. It means to say he has a sober entity and you will appeal to his mind. [...] You cannot, if a raging lion is coming at you, say "let's sit down and discuss this". You should eat him before he eats you and that's it, otherwise you get eaten. That is exactly the situation which makes rights out of the question. You first have to have an entity with a rational faculty, then (and then alone) you have rights.

Does it mean therefore it's morally proper to do anything you want to animals? No. I would say, if you want to engage in sadistic torture of animals for the sheer pleasure of their suffering, that has no benefit of medical knowledge or food or anything like that —no practical, tangible, objective human-life benefit—, then that is inmoral, you should not do that, you are sick, but still outside the problems of the government to prevent; the government is an agency to protect individual rights, and therefore animals are outside of the problems of the government.

- Leonard Peikoff. A Question and Answer Session, minute 4:23.