James Rachels, answered from the texts and cited to the page.
The Cultural Differences Argument runs as follows. Premise: different cultures have different moral codes. Conclusion: there is no objective moral truth; right and wrong are culturally relative.12 The argument is invalid. The premise is a claim about what people believe; the conclusion is a claim about what is the case.3 The premise is a descriptive observation of disagreement; the conclusion is a metaethical thesis about the nature of morality.
The inference does not go through — the existence of disagreement no more entails the absence of objective truth than the existence of disagreement about the shape of the earth (flat vs spherical) entailed the absence of objective truth about that question. Beyond the invalidity of the inference, the relativist position has further problems.
It commits the moral reformer (Martin Luther King, the abolitionist, the suffragette) to being wrong by definition, since the reformer opposes the dominant moral view of his or her society. It commits us to the position that moral progress is impossible, since "progress" would require a standard external to the changing moral view. It mistakes the surface diversity of moral practices for diversity of underlying values — Eskimo infanticide reflects survival pressures in extreme conditions, not a value-disagreement about the importance of children's lives; the Greek and Callatian disagreement Herodotus describes was about the proper way to honor the dead, with the shared underlying value being that the dead must be honored.
Some values must be shared by all functioning cultures: a culture cannot survive without rules against arbitrary killing of its members, without standards of truth-telling that allow communication, without care of the young who would otherwise perish. Less disagreement than there appears to be.4
Should we always tolerate them? What if the norms of our society favor not tolerating them? For example, when the Nazi army invaded Poland on September 1, 1939, thus beginning World War II, this was an intolerant action of the first order. But what if it conformed to Nazi ideals? A cultural relativist, it seems, cannot criticize the Nazis for being intolerant, if they're following their own moral beliefs.The Elements of Moral Philosophy, pp. 33–34
These three consequences of Cultural Relativism have led many people to reject it. 2.5. Why There Is Less Disagreement Than There Seems to Be Cultural Relativism starts by observing that cultures differ dramatically in their views of right and wrong. But how much do they really differ? It is easy to exaggerate the differences. Often, what seems like a big difference turns out to be no difference at all.The Elements of Moral Philosophy, p. 37
In other words, even if the premise is true, the conclusion might still be false. The premise concerns what people believe—in some societies, people believe one thing; in other societies, people believe something else. The conclusion, however, concerns what is really the case. You cannot deduce what is true merely from knowing what people believe.The Elements of Moral Philosophy, pp. 34–35
Some social customs are, indeed, merely arbitrary, and when these customs are at issue, it is fruitless to insist that one society's practices are better than another's. Funerary prac- 119 tices are a good example. It is neither better nor worse to bury the dead than to burn them.The Legacy of Socrates, p. 119
The cultural-relativism critique is Rachels's most-taught position and broadly accepted in contemporary analytic philosophy of ethics. The contested ground is not whether the inference from disagreement to relativism is valid (the consensus agrees with Rachels that it is not); it is whether the cross-cultural moral judgment the critique licenses is itself ethically justifiable, given historical Western moral imperialism and the genuine difficulty of judging practices from outside the cultures that produced them. The Elements Chapter 2 critique stands; the practical politics of when and how to criticize other cultures' practices is a related but distinct question that the chapter does not fully resolve. The position defends the critique as the standard Elements version, engages Sumner and Benedict by name, and acknowledges the hard cases (female genital cutting, honor killings) as genuinely difficult — not because relativism is true but because cross-cultural moral judgment requires care.