The thing with health – and the problem with the health-morality analogy – is that one can have exhaustive knowledge of the facts about health, and the facts about what one ought to do to be healthy, but they can still rationally (if imprudently) say “so what?” There is nothing about the facts of health that compel one to pursue health, nor that condemn that individual as being irrational if they don’t value health and go off and guzzle doughnuts.
Likewise, someone could have exhaustive knowledge of all the facts about wellbeing (assuming it’s even possible) and still say “so what?” Yes, this person is perhaps acting imprudently, but there’s nothing rationally binding about these facts that commit them to pursuing wellbeing.
This is basically a revival of the open question argument and is open to all the worries an open question argument can engender. A big worry that always arises with open question arguments, for instance, is whether the argument begs the question. In this case the worry definitely does arise: if there are moral facts about health (which, if they exist, would have to be included in the set of all facts about health), then there might well be facts that "compel one to pursue health," so saying there aren't seems to beg the question against Harris. If we leave out moral facts altogether, then all the argument says is that medicine is not ethics and it just flat out asserts that Harris is wrong; thus the question is begged another way, since from a claim that Harris need not deny we get without any apparent intermediary steps that Harris is wrong.
The third alternative is to deny that moral facts are not the sort of thing that can compel. This could be done in two ways: either we could be rejecting the notion that the facts to which Harris appeals could even exist, in which case we are begging the question in a third way, or we are saying that they do exist but simply lack the power to "compel". In any case, the argument would boil down to this power to compel.
So what is this missing compulsion-power? Dean gives several characterizations of it: morality compels, it rationally binds, it has practically-motivating punch, it involves worthiness for pursuit; a review to which he appeals of Bloomfield's Moral Reality, which also uses the analogy, calls it a "certain kind of practical authority" and says that morality "demands a certain evaluative response from us irrespective of our interests," and in particular "demands that we be motivated." Now there are three things that are immediately obvious here: (1) it is not in the least clear that these are all the same thing; (2) the characterizations are metaphorical; and (3) they strongly suggest, and in some cases clearly require, a fundamentally deontological account of morality. It is deontologists, believers that morality is at root nothing more than rules or the like that carry their own force with them, who make a big deal about practical necessities, binding obligations, the demands and authority of moral claims, that cannot be reduced to a purely utilitarian or virtue-ethical analysis. (If one allowed utilitarian reduction, the criticism would lose all force, because Harris is a utilitarian. If one allowed virtue-ethical reduction, it isn't clear at first glance why a utilitarian couldn't do something similar.) It is deontologists who demand that morality be something other than interest, rising above all interests and overriding them somehow. It is utterly unclear why Harris is now only allowed to have succeeded in showing that morality is thoroughly a matter for scientific study if he can show that moral science proves deontology right. This comes entirely out of nowhere in a number of discussions, and is never, ever, ever justified.
Nonetheless, suppose we set this aside and instead of assuming deontology here, we simply say that, whatever it may be, Harris can't get the magic oomph, the punch, the force, that makes morality bossy and demanding. We need to say what it is. For it is certainly the case -- and it has been known since at least Plato -- that people can take morality at its face and still, in Dean's phrase, ask "So what?" Glaucon, for instance lays out some suggestions for the grounds on which someone might well say such a thing in the face of the demand to be just in Book II of the Republic. Nor was it a purely theoretical exercise. So either there is no special oomph to morality, or it can't be the mere fact that someone can say, "So what?" that causes the problem here. There is nothing about morality that literally compels people to follow it, or even to recognize it, since if there were everyone would have to follow it, and that's certainly false. Anyone can shrug in the face of a moral 'demand'. So we can't just rest satisfied with saying morals compel; we need to establish that this purely metaphorical compulsion can't itself be reduced to interests, or facts about well-being, or the like. We need to define this oomph that morality can give just on its own, that is such that in the moral case it can't be chased away by the question, "So what?" A categorical imperative? A transcendental good? Or something else? Otherwise we aren't really saying what's being left out of Harris's proposal.
Dean goes on to argue as if his argument showed that "the lynchpin of morality – the commitment to pursue health/wellbeing – have no foundation in scientific fact, only in our own agreement to pursue them." Coming to this conclusion seems to require that the oomph is based on agreement. But that obviously won't work: we can ask "So what?" of any agreement, and these agreements are just sociological, or depending on your exact view perhaps at least partly biological, facts. And likewise, if we accept Dean's further conclusion, "Morality is really a deep kind of prudence: if you value wellbeing, do X, and demand that others do X too," the oomph has vanished away. (And put in this conditional form there's nothing to press toward the anti-realism that Dean says Harris should be advocating, because it can be seen as a problem-solution pair: problem: to find the action that maximizes well-being, solution: X. And there's nothing about that that's particularly problematic for a moral-science realist: physics, chemistry, biology, and other sciences are filled with such problem-solution pairs. That's how Newton built his physics, in fact. Now, realism/anti-realism debates are tricky, but it seems a bit abrupt to say that something that lots of realists think should be interpreted in a realist way strongly suggests anti-realism is right. Only if morality isn't of this conditional form could there be anything that could possibly gum up the works of Harris's project. That's why the oomph, if it delivered on all the promises, would be a problem. But we have no reason to think that the oomph wouldn't equally be a problem for moral anti-realism, most versions of which don't have any obvious room for an oomph transcending all interests, placing demands and compelling, which cannot possibly be ignored, none of which sounds particularly anti-realist.) Either the oomph really exists, in which case Harris does have to account for it because everyone has to account for it, in which case it's pretty crucial to know what it is so that we can actually see that it might be a problem; or it does not exist, and it's difficult to see how this nonexistent thing could cause problems for the health analogy or, indeed, for anything in Harris's project.
This is all very brief, really; in spite of the short space of the argument, there are a lot of issues raised, not all of which I could do justice to in a a post on a blog. But (while I don't think this is true of all of them) most of the criticisms raised against Harris either are too indiscriminate (which is what Harris is using the health analogy to argue) or are have-your-cake-eat-it-too (posing a problem for Harris that magically shows up only for Harris and not the objector, on no identifiable principle) or are really attacks on Harris's utilitarianism and are thus not the criticisms of the basic theses on moral science that they claim to be. The last of these three can generate legitimate objections to Harris, but it's also precisely the point at which critics should stop pretending that they are in uncontroversial territory in formulating their criticisms and that Harris's argument just obviously falls down because of them.