Boghossian starts by noting that people today are relativists about motion (as in Einstein's theory of special relativity) but eliminativists about witches. That is, we think those who condemned and executed the "Salem witches" were just wrong about the existence of people with supernatural powers.
So, is morality more like relative motion, or more like witchcraft? If we give up on absolute morality, can we hang onto a relativistic version of morality, or should we just eliminate moral concepts and language? Boghossian claims that there's no coherent way to retain a relativistic view of morality.
The trouble is that while “Eating beef is wrong” is clearly a normative statement, “Eating beef is wrong relative to the moral code of the Hindus” is just a descriptive remark that carries no normative import whatsoever. It’s just a way of characterizing what is claimed by a particular moral code, that of the Hindus. We can see this from the fact that anyone, regardless of their views about eating beef, can agree that eating beef is wrong relative to the moral code of the Hindus.
I think there's a flaw in the argument here. “Eating beef is wrong relative to the moral code of the Hindus” is merely a descriptive statement if made by a sociologist writing a journal article, but if made by a Hindu father to his Hindu son, it might mean much more than that. You can't just take a phrase like that and abstract it from its context: with moral claims, context is crucial. In the context of a father giving his son a chewing-out, the same phrase might carry a heavy non-cognitive burden: "This is the way we do things and you had better act in accordance with it!"
(It carries the further implication, "If you eat beef, you are not a Hindu." Which is to say, "If you eat beef, you are no longer one of us." This shows the implied threat behind moral rules: disobey, and you will be ostracized.)
Basically, I don't think we can make a sharp distinction between moral claims that are absolute, and therefore normative, and those that are relative, and therefore merely descriptive. Relative claims can carry normative weight, too.
We can see this at work in the objection Boghossian considers: what about etiquette? Aren't we all relativists about etiquette? Don't we all accept that it's OK to slurp one's soup in China, but not OK to do so in Buckingham Palace?
The reason is that our relativism about etiquette does not actually dispense with all absolute moral facts. Rather, we are relativists about etiquette in the sense that, with respect to a restricted range of issues (such as table manners and greetings), we take the correct absolute norm to be “we ought not, other things being equal, offend our hosts.”
This norm is absolute and applies to everyone and at all times.
But there's a problem with this response. Why should we take “we ought not, other things being equal, offend our hosts” as an absolute norm? Why not take it, instead, as the goal in an end-relational sense? "In order not to offend your hosts (at Buckingham Palace) you ought not to slurp your soup."
Again, it all comes down to context. If I am visiting Buckingham Palace I will likely want to avoid personal embarrassment and want to avoid offending my hosts. On the other hand, if a UK political dissident is visiting Buckingham Palace and wants to create an embarrassing situation, he will follow a different dictate, "In order to offend your hosts (at Buckingham Palace) you ought to slurp your soup."
To my mind, this is a much more satisfactory solution. Etiquette is anchored to the social context, and purely practical questions arising from that context, rather than to some free-floating absolute morality that remains unexplained.
So why not morality, as well?