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Tom Regan makes the following argument against one form of cultural relativism. since there are many definitions of cultural and ethical relativism, this argument would not apply to all forms.

One way of arguing that a proposed principle is inconsistent is to show that it implies that the very same act can be both right and wrong. One (but by no means not the only) interpretation of the view called ethical relativism has this implication. On this interpretation, an act is right or wrong whenever the majority in any given society approves or disapproves of it, respectively. It is important to be clear about what, on this interpretation, ethical relativism comes to. The claim is not that a given act is thought to be right in a given society if the majority approves of it; not is it that the act of which a given society's majority approves is right in that society; rather, an act is unqualifiedly right, according to the interpretation presently under review, whenever the majority of the members of any given society happen to approve of it.

This way of viewing right and wrong does imply that the very same act can be both right and wrong. To make this clearer, suppose that the majority in one society happens to approve of killing and eating foreigners, while the majority in another society happens to disapprove of it. Then it follows, given the interpretation of ethical relativism we are discussing, both that (a) killing and eating foreigners is right, and that (b) it is not the case that killing and eating foreigners is right. The principle implies, that is, that both (a) and (b) are true. However, since (a) and (b) are inconsistent, they cannot both be true. Neither, then, can ethical relativism, as understood here, be a valid ethical principle. [Tom Regan, The Case for Animal Rights, p. 131]