The question is here about human desires that are presented as natural rights andtried to be presented in national legislations. This issue is particularly importantbecause of the confusion and anthropomorphic projection that entails betweenthe duties of humans and the alleged existence of rights in animals. The five mainand current positions on animal rights are presented. It is then passed to analyzethe notions of right and duty, then distinguishes the subject of duty and the subjectof the right. The position of Gustavo Ortiz Millán on the rights of animals,and on the quality of being a person according to Daniel Dennett is analyzed and criticized. It concludes by reaffirming the remarkable distinction between owning(natural rights) and attributing (positive) rights that unfortunately are not clarifiedin the Universal Declaration of Animal Rights approved by UNESCO andthe UN.