James Rachels is a Professor of Philosophy at the University of Alabama. In 1978 he wrote a book titled Elements of Moral Philosophy. In this he wrote a passage called "The Challenge to Cultural Relativism".
Rachels felt that Cultural Relativism should not be taken seriously because there would be several different consequences to that.
The theory of cultural relativism says that no customs belonging to a culture can be seen as being either good or bad in the eyes of a person of another culture, simply different, threefore there is no objective right or wrong answer. Rachels thinks that this can't be true in all cases, for example;
One culture thinks that the Earth is flat. Another culture thinks that the Earth is round, therefore there is no objective truth in this matter.
The problem with this statement is that there is a right and wrong answer. Simply because one culture denies the spherical nature of the Earth doesn't make it any less real, so looking at everything in this manner can't be seen as correct and would lead to several problems.
Rachels lists three main problems,
We could no longer say that the custom of other societies are inferior to our own.
While this seems like a statement that doesn't cause problems, it can in extreme situations. If we no longer looked at any customs as being wrong we could not say that apartheid was wrong. We could not say that slavery or anti-semitism was wrong either. See the problem?
We could decide whether actions were right or wrong just by consulting the standards of society.
This means that if we were in South Africa and asked someone if apartheid was wrong they would have to say that it wasn't, because they couldn't judge any society. This leads to the the third problem...
The idea of moral progress is called into doubt.
If we can't judge any society, even our own, then we can't fix anything that is wrong in society.
Rachels finds that another problem with Cultural Relativism is that cultures really don't differ that much when taking a closer look. An example he uses is looking at a poor country where most people refuse to eat cows, even when they are abundant. We see this as a difference in customs, but really they don't eat the cows because they feel that people are reincarnated into cows. So really they are refusing to eat other people, and that is a custom we also hold, the only difference is whether or not we think that the cow could be a person.
After all is said and done Rachels does say that there are good points to Cultural Relativism. We should not judge other cultures unfairly, we should keep open minds towards others.
(I do not necessarily belive in Rachels' philosophy, but was looking him up for a paper, and decided to write down what I found. Some of this is quoted directly from Elements of Moral Philosophy, pg. 15-29)