Assume a discussion between someone who believes in objective moral facts of some sort (however conceived) and someone who who believes that there are no such facts, and that as a consequence any first-order moral judgments are an error.
The error theorist observes the vast differences between what different times and different places regard as right and wrong. He says there is an "argument from relativity," leading to a presumption against moral facts existing at all.
The moral realist replies that one cannot make this inference. After all, there are people who believe in a hollow earth, or a flat earth. It does not follow that there are no geological facts, only that people are subject to small and large errors about them.
To this an error theorist might reply -- oh wait, let's quote exact words here.
"The argument from relativity has some force simply because the actual variations in the moral code are more readily explained by the hypothesis that they reflect ways of life than by the hypothesis that they reflect perceptions, most of them seriously inadequate and badly distorted, of objective values."
As regular readers of this blog will surmise, I disagree with Mackie here, but I think the quoted sentence is a good concise statement of his argument so for now I'll just let it stand.