I guess the big question for relativism is whether a culture or society's basic moral principles could be wrong or false. According to relativism this is impossible. Societies from the Egypt of the Pyramids to the antebellum South practiced the enslavement of other human beings. Were those societies making a moral mistake? Was there something they didn't realize about people and their rights that they should have?
Or, let's try this statement from our Declaration:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain Inalienable Rights, that among these are Life, Liberty, and the Pursuit of Happiness.
If liberty is impossible where there is enslavement, then if this sentence is true, then the practice of enslaving people is wrong (a point that, notoriously, was not put into practice by Jefferson himself, who was himself a slaveowner). The Declaration says that we have rights regardless of what society says. If relativism is true, the society giveth rights and society taketh rights away. There is nothing you can appeal to over and above society that says that we really have rights that our society is denying us.
If there are no objectively binding moral obligations, then there are no objectively binding human rights, because rights logically entail moral obligations on the part of people who are expected to respect those rights.