>One of the main arguments for moral anti-realism is that there is no way
to objectively verify or falsify moral claims. For example, it is not
possible to conduct a scientific experiment to prove that murder is
wrong or to measure the “goodness” of honesty. This contrasts with
scientific claims, which can be tested and verified through
experimentation and observation.

This is technically an argument from incredulity. Even if we may not currently know how to objectively derive moral facts (although I would posit the method I have posted in this thread as a possible candidate for such), this does not imply that no such method can be found in the future.

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>Another argument for moral anti-realism is that moral beliefs and values are culturally relative and vary widely across different societies and
historical periods. This suggests that moral beliefs are not based on
any objective moral facts, but rather on the cultural and historical
context in which they are held.

The fact that there are various different models of an alleged phenomenon each contradicting themselves does not preclude the existence of such phenomenon. Otherwise we would have to discard the spherical earth theory because there were so many different models of the earth in the ancient past. We would also have to discard the theory of evolution because of all the creation myths that people held even to this day. It is possible that only one person's/culture's morality is correct and all the others are wrong, or at least there might be a variation in the merit of moral claims.

The set containing all moral codes one can devise is at least limited by sustainability. Those moral beliefs that wipe out any holder of such beliefs tend not to last long. Furthermore the more parochial a moral system is, the less likely a group of its adherents can expand beyond a limited time and space without discarding such beliefs.

There is also the fact that, just like descriptive fact systems, prescriptive systems can be corrupted by agents bending such system to their personal benefit. The variation in moral beliefs from a possible true one may be due to corruption of people's moral understanding.

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>Another version of moral anti-realism is called relativism, which holds that
moral statements are true or false relative to a particular culture or
society. According to relativism, there are no objective moral facts or
values that hold true across all cultures or societies.

What if one culture clashes with another? For instance, what if a group of people believes that they are morally obligated to have sex with another group who themselves believe that they are morally obligated to maintain celibacy? Both culture's morals cannot both be practiced. At a bare minimum, freedom from association will be required in order to avoid conflict and for moral relativism to work which would make freedom from association an objective standard. The same can be said of moral subjectivism where a particular society/culture is a culture of one individual.

I am unsure about expressivism. Moral beliefs not extending beyond opinion doesn't seem that different from moral nihilism.

>Moral anti-realism has been criticized by moral realists, who argue that
it fails to provide a coherent account of moral language and ethical
reasoning. They argue that moral anti-realism is unable to explain how
moral statements can be meaningful or have any practical implications if
they do not correspond to any objective moral facts or values.

I'll have to side against the moral realists in this case. Although moral statements do have to be objective in order to work (the sex mandate group and the celibates can't both be right), this does not imply that they exist/are_real. Also the existence of language used to describe a given phenomenon does not prove the reality of that phenomenon, other wise the language of faster than light travel found in many sci-fi genres proves that you can travel faster than the speed of light.

That being said, people have desires, wishes, and other preferences. Such preferences take the form of prescriptive type phenomenon. Although these preferences can contradict one another, they can possibly be used to derive a consistent objective meta-preference given the right framework.