Cultural relativism rests primarily on five major assumptions. First, we must recognize that most cultures have their own moral codes. For instance, while it might be normal within some cultures to bury the dead, it might be more normal in a different culture to burn a dead body (or even eat them, as Rachels and Rachels observe). Second, within any culture, the moral code determines right and wrong for the individuals who live in that culture. Using the earlier example, we can imagine a group of people who feel that it is sacrilege to burn (or eat) a body, although for a different group, it may be a normal action. Third, if it is the case that right and wrong vary from culture to culture, then there is no objective way to judge what counts as a correct moral code. Fourth, we should recognize that whatever moral code we subscribe to, it is not special. There are plenty of moral codes out there that have equal weight. As such, this leads to the final assumption of cultural relativism: we should not judge other cultures for their moral assumptions, and we should approach cultural norms outside of our own with openness and tolerance.
Rachels and Rachels do some work to dismantle these arguments, however. Possibly the strongest argument against cultural relativism is the possibility (and reality) that some cultures are morally intolerant of other cultures. If we are tolerant of the moral codes of all cultures, we need to be tolerant of those cultures that believe themselves to be morally superior to other cultures, such as Nazis. Nazis, for instance, believed that they had a moral right to invade other countries and kill various minority groups. This, as well as other instances of intolerance, must be tolerated by cultural relativism, and thus intolerance is able to thrive under the imperative of tolerance.
Another argument is that just because different cultures disagree does not mean that there is not an objective morality that exists. We see, for instance, in some parts of the world, people believe that Earth is flat. Others do not. But this does not mean that there is no objective truth about the shape of the planet. Therefore, just because there are different beliefs about morality does not mean that an objective truth does not exist. On top of this, Rachels and Rachels argue that some societies do share certain values (e.g., caring for young, restricting killing), and if we believe that progress can be made (for instance, the abolition of slavery or the civil rights movement), we have to believe that some moral codes are better than others.
In the end, Rachels and Rachels provide what might be a pragmatic argument for morality, one that promotes social welfare. However, there are some issues with their claims. To their first point, it is possible that tolerance must remain a kind of meta-principle or imperative, one that cannot be shirked from culture to culture. It is also possible to scrutinize some of their other arguments. For instance, they claim that just because there are opposing viewpoints on morality does not mean that morality cannot be objectively true, and they provide the flat Earth argument as an example. However, their example uses a physical entity as proof that one of two opposing sides can be objectively true. This may be a false analogy, as morality is a social construct more than a physical entity. Additionally, in trying to prove that there can be an objective morality, they show examples of moral progress in cultures, which supposes a "better" and therefore more objective morality when attempting to prove their statement. In short, Rachels and Rachels assume the very premise that they are trying to prove.