Why and how does cultural relativism mitigate ethnocentrism? Is cultural relativism desirable?
"Cultural relativism" can mean several different things, and much of the debate over its desirability can be traced to this ambiguity. Descriptive cultural relativism is basically undeniable: Cultures do, in fact, differ in their social and moral norms. But normative culture relativism is not as obviously true: It isn't clear how, if at all, our treatment of people in different cultures should vary based on their culture's norms. So the normative sense of cultural relativism that says we ought to judge other people by the standards of their own culture could be right, but isn't necessarily.
There is also methodological cultural relativism, which is a method that many sociologists and anthropologists use to sort of temporarily suspend judgment about other cultures until they get all the facts in. This is probably a good thing, but it's a very weak sense of relativism; in the end they still go home and publish in Western academic journals according to Western cultural norms. It doesn't even require any particular relativism: You can just have the norm in your own culture that you don't judge other cultures until all the facts are in.
"Ethnocentrism" can also be an ambiguous word. It normally means something quite negative---the tendency to view people of your own culture as inherently superior and people of other cultures as inherently inferior. It frequently results in hatred and even violence. But sociologists also use "ethnocentrism" in a sort of technical sense, to mean simply that we judge people of other cultures by the standards of our own culture. This latter is not obviously wrong---one culture's ideas can in fact be more correct than another's, and it may turn out that we happen to live in the culture that has the best ideas.
I think a key point to keep in mind here is that it matters why you are using the moral standards you are. Is it simply because you grew up with them, and never questioned them? That is probably ethnocentrism. But have you actually analyzed those norms, challenged them, confronted them with evidence, and yet they still held up? Then what you are doing is definitely not the negative kind of ethnocentrism, though it may be "ethnocentrism" in this broader more technical sense.
Indeed, it's not clear that the strongest form of normative cultural relativism is even coherent. Most cultures are not cultural relativists; that is, most people in most cultures do not think that one should judge others only by the standards of the others' own culture. They think that their standards are the objectively correct ones that everyone should use. So in order to be a cultural relativist, you need to judge people only by their own culture, but the only culture that actually tells you to do that is your own culture, namely the subculture of Western academic sociologists. So you are in the end still judging based on your own culture, and you are still faced with the question of why your culture's norms are better than anyone else's. Or in fact you could justify being an imperialist, because Western culture has a historical tradition of imperialism and you could simply be acting according to the norms of your own culture---so how can anyone judge you as wrong?
Yet I understand where normative cultural relativism comes from; it is an attempt to respond to, and in some sense atone for, the extreme violence and destruction created by colonialism and imperialism. One of the things that our imperialist forebears did was judge other people based on their own culture, so if we don't do that, maybe we won't be imperialists! But that doesn't actually follow. That wasn't what made them imperialists, and indeed getting rid of it doesn't necessarily stop us from being imperialists.
A much better approach in my opinion is the concept of universal human rights. By a gathering of global consensus (or something close to consensus), we have established global human rights principles such as those set down in the UN Charter. These are rights that everyone agrees everyone should have. Furthermore, these rights are precisely the sort of rights that explain what is wrong with colonialism and imperialism. What made our forebears imperialists was not that they judged according to their own culture, but that they violated (what we now recognize as) universal human rights. Yet ironically many cultural relativists actually oppose universal human rights, arguing that they are somehow imposing Western values on everyone else---something that I think many of the people from non-Western cultures who helped design and ratify the UN Charter may find baffling.