If moral realism (the notion that moral values exist independently of human minds) is false, then there is no reason to talk of “morality” as if it were something distinct from personal preference. Given moral relativism, moral beliefs are just personal/social preferences. What we call “morality” is nothing more than a set of personal preferences regarding certain dispositions and behaviors, or a set of normative social preferences – both of which are subjective in nature and can change over time. Saying “vanilla ice-cream is better than chocolate ice-cream” and saying “telling the truth is better than lying” are the exact same kind of claims: personal, subjective preference. No oughts are involved. They are just autobiographic or (to possibly coin a new term) sociobiographic statements. They describe rather than prescribe.
If moral relativism is true, then saying “one ought not kill other people without sufficient justification” just means “we prefer that you do not kill other people without sufficient justification.” If someone has a different preference, and chooses to kill other people whether they have justification or not, they haven’t really done anything objectively wrong. They are merely being socially unfashionable, sort of like wearing white socks with a black tuxedo. We might even deem them socially undesirable, like the person who demands to collect $200 without passing go. We’ve all agreed that one must pass go first, and don’t like anyone trying to play by their own “house rules.” We can punish them for disregarding our preferences and choosing their own, but that is just our preference as well. No real moral wrongdoing is involved.
If the category of “morality” is indistinguishable from the category of “personal preference,” then there is no basis for, nor reason to speak of “morality” as a distinct concept. Moral beliefs/behaviors are just personal/social preferences, so moral relativists should cease thinking and speaking in terms of morality.
I think most people will recognize that moral claims are not just preference claims. Moral beliefs are qualitatively different from mere preferences. When someone kills another human being without sufficient justification, we recognize that they have not merely chosen a different preference, but have done something objectively wrong. That is why we call one’s preferences in food “opinion” and their choice to murder another human being “immoral.” The former is a subjective personal preference, while the latter is an objective moral truth.