The major argument for ethical relativism is that people and their values and attitudes are very heavily influenced by their cultures. This means that their ethics cannot really be the product of any universal values. Rather, their ethics are creations of their various cultures.
If our ethics are created by our cultures, then we cannot really believe that people from other cultures are bound by them. We do not, for example, think that it is wrong for other people to wear different clothes or eat different foods. These things are simply cultural choices. So too, a relativist would argue, are ethics. The idea that every individual should have freedom of speech, for example, is simply an artifact of Western culture, not a universal truth that should be imposed on all cultures and societies.