The article deals with the approach of the right-wing libertarian, anarcho-capitalist, Murray Rothbard to the issue of animal rights. The author offers a critical analysis of his dismissal statements in the work Ethics of Liberty. He deals with Rothbard's arguments and confronts them with the arguments of Peter Singer and Gary Francione. The author pays special attention to Rothbardʼs argument from the nature of animal warfare, which is one of the reasons for Rothbardʼs view on animal rights. Based on a hypothetical example of beings from another world, which Rothbard himself mentions, the author refutes his argument and points to the problem of inconsistency in Rothbardʼs thinking. Given that this argument is not (and cannot be) a central argument for Rothbard, the author then focuses on Rothbardʼs central argument from the very notion of the concept of a right. The difference between Rothbard and Francione is, in this respect, conceptual (each of them works with a different understanding of the concept of a right). The difference between Rothbard and Singer is basically paradigmatic. In this context, the author points out that both anarcho-capitalism and utilitarianism are reductionist theories and considers the need to find a non-reductionist solution. However, in the controversy, he leans to the side of Singer, due to the moral inadmissibility of Rothbardʼs assumption of the priority of individual freedom over relevance of any moral good or evil (under the respect of persons but not of other sentient beings), which cannot be understood other than Rothbardʼs ethical thesis.