Moral relativism is a fact in the world we live in. Each person inevitably constructs his own set of morals, his own system for judging what is "good" and "bad", "right" and "wrong". Even if one were to believe that morality was not relative, that there was "objective morality" of a divine presence, he would not know what those"objective morals” were. He would not be able to definitively state what acts were "objectively good" or "objectively bad" since we have no way of divining god's morals. This leaves us in a world of moral relativism even if we believe there is a divine moral standard.
Each person creates their own sense of morality. There are a few base propositions upon which larger moral structures can be erected. Ideas like ultilitarianism (the greatest good for the greatest number is the most desirable), master-morality (as opposed to slave-morality, Nietzscheian morality), nihilism, or hedonism define what is most valuable in this world, and are ideas around which a larger sense of morality can be constructed. Religions also provide such core ideas; belief in the god of the bible or the Koran, or belief in any god who was good enough to author a book, provides a person with something more concrete, though undoubtedly also man made, on which to base moral principles. Whether a person sees god, mankind, or himself as the most important thing in the universe, his sense of morality will shape itself to protect the thing most valued. When we act in a way that we recognize as detrimental to us individually, but we still think is "right", it is because we are placing ourselves below something we value more. Though these values might be somewhat abstract, they produce in us a sense that we are not more important than others, that our wants and needs are not supreme.
Does this mean that one person cann't say that anothers acts are "right" or "wrong" since their morals are subjective? I say no. A person can say acts are "good" or "bad" since they consider how the acts will affect something, hopefully something other than themselves, that is not subjective. An act can be bad for humanity or "bad" because it creates unnecessary sorrow in the world. Our reasoning for why such an act is morally "wrong" is solid as long as what is considered valuable is shared. Someone who values something else more, say themselves or even their country or religion, might view such a morally questionable action as "right". Everyone values something (nihilists excluded), so everyone will have an opinion on moral issues. People who value the same thing will agree on most issues. Our evolution as social animals has left us with most people agreeing on most issues, especially the major ones (murder, rape, theft, ect.).