Here. Although I think he overcomplicates the issue. The real question for me is, why this obsession with justification in the first place?
Yes, secularists (I wouldn't say atheists... I'd think this applies to anyone who grounds their sense of ethics outside of religious mandate) have a tough time "justifying" morality. As Douthat (who Smith quotes) notes, there is no absolute human equality in evolutionary theory (quite true). But the whole point is that non-secularists have a tough time offering a reasonable justification too, they just don't seem to realize it.
"It's written in a book - that's the justification". OK. So if secularists point to a book that has their moral code in it, we're all cool? Of course not. All communities maintain their own constructions of the way the world works. Within a given community, of course that construction is taken as valid. But to someone outside the community, the non-secularist hasn't given solid justification at all! Think, for example, about white supremacists who ground their ethics in the Bible (and there is some pretty xenophobic stuff in there). Do we say that they have thoroughly justified their views? No - we think there are a lot of problems with that!
It seems to me that secular ethics distinguishes itself by recognizing the fundamental pluralism of society, and that while these community-level constructions of the world are useful for getting along in the world, in a community - they don't quite reach a standard of justification they claim for themselves. So we need a broader, more pluralist ethics and Douthat is right - that often consists of dismissing the justificationist, foundationalist project itself. Why? Because an ethics that you can get by writing a poetic book and waiting a couple centuries for it to gain mystical significance does not seem like a very laudable ethical code. You'll get some gems from that approach, of course. We humans learn how to get along with each other, and that is going to be distilled in these various books. But it's not a very strong justification. What much of the world has converged on is that since within-community justifications don't work outside of the community, we need to come up with an ethical orientation that allows the coexistence of multiple potentially contradictory communities, justification and foundation be damned. This is liberalism.
Another way of putting it is this: have an orthodox Jew tell someone who is deeply anti-circumcision like Andrew Sullivan that circumcision is morally jutsified. Have an orthodox Muslim tell an American that practically enslaving women is morally justified. Have an orthodox Christian tell a homosexual that they are beyond the pale of moral justification. Get the six of them (the Jew, Andrew Sullivan, the Muslim, the American woman, the Christian, and the homosexual) together in a room together to talk about this stuff, and then try and tell me with a straight face that non-secular ethicists have a solid justification for their ethics. They don't. The beauty of secular society (and I want to clarify - that does not mean "atheist society") is that it recognizes that you can't provide an ultimate foundation for these claims. They are claims about how society ought to live together, and they are claims that we assert based on our experience with the sort of society we'd like to live in - not claims that we can justify with proof or citation.