lukeprog gave a list of metaethics questions here:
What does moral language mean? Do moral facts exist? If so, what are they like, and are they reducible to natural facts? How can we know whether moral judgments are true or false? Is there a connection between making a moral judgment and being motivated to abide by it? Are moral judgments objective or subjective, relative or absolute? Does it make sense to talk about moral progress?
Most of these questions make no sense to me. I imagine that the moral intuitions in my brain come from a special black box within it, a "morality core" whose outputs I cannot easily change. (Explaining how my "morality core" ended up a certain way is a task for evo psych, not philosophy.) Or I can be more enlightened and adopt Nesov's idea that the "morality core" doesn't exist as a unified device, only as an umbrella name for all the diverse "reasons for action" that my brain can fire. Either perspective can be implemented as a computer program pretty easily, so I don't feel there's any philosophical mystery left over. All we have is factual questions about how people's "morality cores" vary in time and from person to person, how compelling their voices are, finding patterns in their outputs, etc. Can someone explain what problem metaethics is supposed to solve?
Another answer (which I'm not sure is the answer) is that in logic or mathematics, a person is more likely to be convinced by a random correct proof than a random flawed proof; and if a person is convinced by a flawed proof it is easy to change their mind by pointing out the flaw in the proof; but if a person is convinced by a correct proof, then it is difficult to change their mind by incorrectly claiming there is a flaw. Of course I am being sloppy and nontechnical here; I bet there is a subtle, technical sense in which, under reflection, Modus Ponens is more appealing than Appeal To Justin Bieber.