What is the moral diversity agrument for nonobjectivism, and how do moral objectivists attempt to answer it?

Richard Boyd states that Moral Realism (Moral Objectivity)
asserts as true that:

1. Moral
   statements are the sorts of statements which are (or which express propositions which
   are) true or false (or approximately true, largely false,
   etc.);


2. The truth or falsity (approximate truth...) of
   moral statements is largely independent of our moral opinions, theories,
   etc.;


3. Ordinary canons of moral reasoning—together with
   ordinary canons of scientific and everyday factual reasoning—constitute, under many
   circumstances at least, a reliable method for obtaining and improving (approximate)
   moral
   knowledge.

(Boyd,
Richard N. (1988), "How to Be a Moral Realist", in Sayre-McCord, Geoffrey,
Essays on Moral Realism, Cornell University Press, pp. 181–228,
ISBN href="http://en.wikipedia.org/wiki/International_Standard_Book_Number"/>
0-8014-2240-X)

In other words, some things are right or
wrong no matter how anyone feels about the rightness or wrongness of
them.

Non-objectivists argue that for every premise that an
objectivist asserts to be true, largely true, false, or largely false, there are others
who assert differently or oppositely.

Non objectivists
argue that the mere existence of controversy over moral issues proves that there can be
no such thing as moral facts, absolutes or truths. They point out that in similar
circumstances people with different perspectives, who come from different cultures or
who have differing degrees of ignorance on the issues involved may act in very different
ways and justly view each of these different responses to the issue as equally moral or
even more moral than another.

Objectivists or Moral
Realists counter this argument with the fact that even in the empirical realm there is
much disagreement--sometimes very deeply-held and widespread disagreement, but that does
not prove that there cannot be a single, factual
answer.

For example: evolution or the spontaneous origin of
the universe is widely and fervently disputed by creationists. While the presence of a
religious element might tempt the researcher into believing that this is a moral or
religious argument, the fact is indisputable that whoever is correct, whether
evolutionists or creationists, there can be only one factual beginning of the real
universe in which we live. Either it evolved or was created. We may never be able to
prove which one to anyone's complete satisfaction, but that does not alter the fact that
it can be only one.

So, simply because there is controversy
over a moral premise does not in any way disprove that it is possible that a moral
premise can always be either true or false regardless of
opinion.