If I had a nickel for every time I hear something like “Well, if it's right for him, who am I to judge?” I'd still be poor. Not because I don't hear it a lot but because I'd donate all those nickels to charity. Anyway, relativism--the position that values are relative to an individual or culture-is by far the most dominant view among the general population. In fact, back in my pre-philosophical days I too was a relativist. If you were born to a relatively secular or liberal religious household chances are you *think* you're a relativist too.
Before getting into the problems with this view, I'll quickly go over some of the (perceived?) virtues of relativism. (a) It promotes a culture of tolerance and avoids/tempers dogmatism and (b) by way of (a) it can reduce conflicts. However, there are two main problems with relativism: (a) no one really believes it when push-comes-to-shove and (b) it's logically incoherent: instead you must pick either realism (there are objective values) or nihilism (there are no objective values).
EDIT: Some commenters have correctly pointed out that realism and nihilism aren't the only positions available if you reject relativism. In the interest of simplicity for my non-professional audience I intentionally lumped non-cognitivist positions in with nihilism. So, for those of you familiar with the distinction, please read "nihilism" as including non-cognitivist positions for the purposes of this post. For non-philosophers, if you'd like to learn about the difference I've given a brief summary here.
Part 1: There Are No True Relativists
OK, let's grant the virtues of relativism for the moment. Unfortunately for relativists (i.e., most Westerns) you aren't really relativists. Relativism leads to the absurd conclusion that there's no normative difference between a sadist's values and a humanitarian's values. Hey, if tormenting people for fun is perceived as good and right by the sadist, then it's good. Who are we to judge his values? The relativist might reply, “No, what I mean is you can do what you want so long as you don't harm other people.” That's a fine response but you've just given up relativism. You've just conceded that there is at least one objective moral truth.
Another response might be that people can do what they want so long as it makes them happy (however you define it). Once again you've conceded the argument because you've committed yourself to the objective value of happiness. I.e., when actions conflict with happiness, we ought to favor happiness; happiness is more important than all other things. You are actually a realist/objectivist.
Again, relativism leads to the unsavory position that the Gestapo and Medicins Sans Frontieres are organizations of equal moral worth. If the Gestapo thinks it's good and right to “throw the Jew down the well,” then, hey, who are we to judge? Punching someone in the face is no less praiseworthy as giving someone a helping hand. I doubt very much that anyone truly thinks that, beyond personal beliefs and preferences, there are no important differences between the values in the above examples. If you think there are important differences you're a realist because you just made a judgment about one set of values having more value than another. If you don't then you're probably a nihilist. But you aren't a relativist. More on that later.
Why the Virtues of Relativism Aren't Virtues
Tolerance, aversion of dogmatism, and reduction of conflicts are not genuine virtues in the face of obvious evil. If we discovered that our neighbors had child slaves most of us do not think it would be virtuous to tolerate the practice. In fact, we should dogmatically oppose it and we should confront those who practice it. In short, most of us think that confronting evil and injustice is virtuous while tolerating it is not. And so, the virtues of relativism are not virtues after all. They are contingent on the objective goodness of the practice in question.
If we think a practice is good or perhaps value neutral then tolerance for diversity appears good. But it's not relativism that grounds the virtue of tolerance, non-confrontation, etc... It's our recognition of a practice that brings about some good. And so, the virtuousness of our response is grounded in the fact that we are tolerant of things that are good (or value-neutral) and intolerant of things that are bad. In short, it is the goodness or badness of the act that grounds the virtue of our response to it.
Part 2: The Logical Invalidity of Relativism and Why You Must Be Either a Realist or a Nihilist
Argument 1: The Multiplicity of Things
Now if a man believes in the existence of beautiful things, but not of Beauty itself, and cannot follow a guide who would lead him to a knowledge of it, is he not living in a dream. Consider: does not dreaming, whether one is awake or asleep, consist in mistaking a semblance for the reality it resembles?
I should certainly call that dreaming.
Contrast with him the man who holds that there is such thing as Beauty itself and can discern that essence as well as the things that partake of its character without ever confusing the one with the other—is he a dreamer or living in a waking state?
He is very much awake.
So may we say that he knows, while the other has only a belief in appearances; and might we call their states of mind knowledge and belief? Republic V. 476
For example, when someone says x was good, y was good and z was good, all these things (are perceived to) share the quality of goodness. And so goodness must be one objective thing, not many things. There is one concept of goodness and particular acts or events can partake, to varying degrees, in goodness. (Note: some philosophers contest this view suggesting that there are only particulars but let's roll with it for now. It's not the only argument against relativism.)
Argument 1: “True”--You Keep Using That Word But I Don't Think It Means What You Think It Means
Person A says “I believe abortion is wrong (in circumstance C), therefore it's wrong.” They say the proposition “abortion is wrong” is true.
Person B says “I believe abortion isn't wrong (in circumstance C), therefore it isn't wrong.” They say the proposition “abortion is wrong” is false.
To summarize: An assertion cannot both be true and false (law of non-contradiction). Relativism violates the law of non-contradiction because some people will say of a moral statement that it is true while others will say it's false. There are two alternative: (a) both are wrong and there is no moral truth at all, just preferences (i.e., some form of nihilism is true); (b) one is right and the other is wrong (i.e., some form of realism is true).
What you can't be is a relativist. Either there are objective moral facts and/or values or there aren't. It's one or the other. It can't be both. People can have beliefs/preferences about what's good/right/bad/wrong but this doesn't tell us anything about the objective state of affairs. If you're a realist, people can have mistaken beliefs about what's good/right/bad/wrong. If you're a nihilist, people only have preferences and preferences can't be “true” or “false” any more than my preference for strawberry ice cream is true or false.