The relativist can offer no cogent reason why we should not simply get on with it

I have little truck for multiculturalists and moral relativists - pin-heads cocooned in safe spaces, which shield them from the evil consequences of their lazy thinking.

Peter Singer gets at one of the contradictions in this passage from One World Now: The Ethics of Globalization, page 163.

This objection is confused. Moral relativists imagine they are defending the rights of peoples of non-Western cultures to preserve their own values, but when moral relativism is taken seriously, it undermines all ethical arguments, including those against cultural imperialism. For if morality is always relative to one's own society, then you, coming from your society, have your moral standards and I, coming from my society, have mine. It follows that when I criticize your moral standards I am simply expressing the morality of my society, but it also follows that when you condemn me for criticizing the moral standards of your society you are simply expressing the morality of your society. There is, on this view, no way of moving outside the morality of one's own society and expressing a transcultural or objective moral judgment about anything, including respect for the cultures of different peoples. Hence if we happen to live in a culture that honors those who subdue other societies and suppress their cultures—and the very same people who defend moral relativism often tell us that this is the Western tradition—then that is our morality, and the relativist can offer no cogent reason why we should not simply get on with it.

The point was neatly made by General Sir Charles Napier, the British army's commander in chief in India in the mid-nineteenth century, with regard to the practice of sati, in which widows were burned alive on the funeral pyres of their husband. When Napier ordered that the practice stop, Hindu priests complained to him that it was their custom, and customs should be respected. "This burning of widows is your custom," Napier replied. "Prepare the funeral pile. But my nation has also a custom. When men burn women alive, we hang them. . . . Let us all act according to national customs."

We should reject moral relativism. A much better case against cultural imperialism can be made from the standpoint of a view of ethics that allows for the possibility of moral argument beyond the boundaries of one's own culture.