If animals have rights, does that not mean that we would have to punish the killing of animals in the same way we do the killing of humans?

No, of course not. It is certainly true that if we as a society ever really accorded moral significance to animal interests and recognized our obligation to abolish and not merely regulate animal exploitation, we would very probably incorporate such a view in criminal laws that formally prohibit and punish the treatment of animals as resources. But that would not mean that we must punish the killing of an animal by a human in exactly the same way that we punish the killing of a human by another human. For example, our recognizing that animals have moral value does not require that we prosecute for manslaughter someone who, while driving recklessly, hits a raccoon. The prosecution of humans who kill other humans serves many purposes that are not relevant to animals. For example, criminal prosecutions allow the families of crime victims to experience some form of closure, and although there is ethological evidence that many nonhuman animals experience grief at the loss of family or pack members, a criminal trial would not be meaningful to them.