Before I discuss that let me quote from his lede:
If you are going to make a moral argument, whether in the seminar room or in the public square, people today expect you to avoid invoking God. Atheists and theists alike share this expectation, with atheists eager to show that their moral knowledge and action are uncompromised by disbelief in God’s existence, and theists eager to establish the rational credentials of their moral convictions and protect themselves against charges of fideism.My very minor quibble with O'Brien is that though he's technically correct that it's logically possible to believe that there are intrinsically evil acts that nevertheless might be warranted in some cases, I think the atheist has no grounds for believing that there are, in fact, intrinsically evil acts.
This expectation is unwarranted, however, because God’s existence is directly relevant to moral knowledge and action: If appeals to God get ruled out, either by disbelief in His existence or reluctance to rely upon it, then it isn’t possible to demonstrate that there are moral absolutes.
A moral absolute is an exceptionless norm against choosing a certain type of action that is intrinsically bad. Recognizing a moral absolute therefore involves two stages of evaluation: first, seeing that some act, such as killing an innocent person, is intrinsically evil, and second, seeing that one ought never to do evil. My contention is that a demonstration of this second stage of evaluation will need to appeal to God’s legislation against doing evil that good may come.
This appeal of course assumes that God exists and that He legislates the moral law. Without this appeal, it remains logically possible for someone to think that there are intrinsically evil acts, and to think that virtuous people will habitually refuse to consider committing such acts, while yet refusing to infer that such acts must be avoided in every situation whatsoever.
It is instructive at this point to consider Aristotle. Aristotle thought that there were intrinsically bad actions that nobody ought to consider choosing, and although Aristotle was a theist, his conception of God was not as a providential creator or moral legislator. Aristotle’s example is noteworthy because it shows that it is possible to arrive at the conviction that intrinsically bad actions exist without appealing to God’s legislation. But Aristotle’s example is noteworthy also because of what he does not try to do, which is to demonstrate the truth of such absolute prohibitions by appealing to some more basic set of moral reasons.I think this is slightly askew, or at least the way O'Brien frames it is a bit unclear. Receiving the correct upbringing may help you to intuit that some acts are distasteful, and you may believe them to be intrinsically bad, but, for the atheist, that belief is non-rational. It's like the conviction that the color green exists in the grass rather than in one's brain. On atheism, evil is not inherent in an act any more than greenness is inherent in the grass. It's an illusion.
For Aristotle...the grounds for absolute prohibitions bottom out in the perception of actions as base and shameless. Such intuitionism is as far as I think non-theological ethics can go. Receiving the correct upbringing will get you to see that certain acts are intrinsically bad, and you ought never to choose them; but in order to go further and demonstrate why this is true, you need to be able to appeal to God’s legislation of the moral law, which is what proves the reasonableness of forbearing from evil in the extreme tight-corner situation.
In order to rationally regard an act as intrinsically bad one must, as O'Brien correctly insists, be able to refer to a transcendent moral authority. Otherwise, no matter how horrific the act may be, it's not morally evil anymore than a shark attack on a child wading in the ocean is morally evil.
It's true, as O'Brien goes on to say, that most people don't realize this, but that's because most people don't think about it anymore than they think about where the color green is actually located. Even so, it needs to be pointed out to the atheist that his belief that he can make meaningful moral judgments is nonsense if God doesn't exist. Whenever he attempts such judgments he's piggy-backing on Christian (or, more generally, theistic) assumptions while at the same time denying that those assumptions are correct.
The moral opinions of non-theists are simply expressions of their subjective feelings and as such have no objective value or weight. They're irrelevant, or should be considered to be such, to our social life and discourse.
Readers interested in the topic should read O'Brien's piece. It's very good.