*The separate evidentiary argument states that it is impossible to offer a good naturalistic account for observed human moral behavior.
I. Even if there were no god, there might still be objective moral standards. There are, of course, objective physical truths that naturalists can account for without a god; perhaps the same might be true of moral standards. Many non-theistic philosophers (and some theistic ones) have offered natural accounts for objective moral standards, notably moral realism. I think these arguments fail, but they fail on epistemic grounds; there is nothing ontologically outrageous about moral realism.
II. Theism does not offer objective moral standards. In the sense of "objective" as "not a property of a mind", theistic morality is established by the mind of god, and ipso facto subjective. In the sense of "objective" as "rationally determinable" (in the sense that it is objectively true, i.e. rationally determinable, that "2+2=4" is a theorem of arithmetic), theism offers no rational epistemic method to determine properties of the mind of god.
III. Even without objective moral standards, we still have a basis for calling things good and bad: our subjective preferences. Of course, a subjective account of morality fails to offer a basis for calling some moral beliefs mistaken or false, but there's no particular reason to require that the good be the true. It's not false or contradictory to say that I disapprove of slavery, and I disapprove so strongly that I'm willing to employ coercion to eradicate, prevent or punish it. If you believe just as strongly that slavery ought to be tolerated, we'll just have to fight it out. An examination of human history — notably the American Civil War — shows that this is actually how many moral arguments have been settled.
That we can and have settled some moral arguments just by talking about them does not entail that there is some objective truth to moral questions. Moral discourse is substantively different from scientific discourse: science relies on falsifiability and evidence; moral discourse relies on compromise, negotiation and propaganda (in the broadest sense of trying directly to change others' subjective preferences). We've developed preferences at an abstract level: We prefer to compromise some of our concrete moral preferences rather than fight about every moral question.
The contradiction in the argument that we would prefer to have an objectivist account of morality and therefore there actually is an objective account of morality should be obvious.