The claim that man cannot be good without God usually makes God the ontological foundation of obligation or the enforcer of moral law, and the denial of the claim consists in arguing that the law needs no such foundation. If we take it like this Christianity criticises both claims since it takes any moral law, especially one divinely founded and enforced, as more of a fundamental human problem. The gospel certainly doesn’t consist in the proclamation of a moral law full stop, and it is absurd to the point of contradiction to think that the good news Christ came to announce to Israel was one a divinely grounded and enforced moral code. Israel already had the perfect form of such a code for a thousand years – its problem was its inability to keep it. Another moral code (Now with new foundation! New enforcement!) wasn’t just bringing coals to Newcastle but to throw them on a burning home. Paul generalizes the problem to the whole world since we’re all born with the moral law in us before it is clarified by Torah, and by the time our choices, bad luck and perverse social structures efface the law from our heart we take it as pointless to proclaim it to us again. As Paul would note later, the law both written in Torah and human nature is good in itself but in our present circumstances it condemns us.
The Christian sees man’s moral need for God as insufficiently in God’s grounding a moral code and formally and ultimately in God’s empowerment of the soul to follow and enjoy the code that God establishes and proclaims. As the Psalm puts it: I will run after you, O LORD, when you have enlarged my heart.
Our present moral muddle about the criteria for human actions (Duty? Consequences? Human flourishing?) occludes the deeper problem that even after we find the criteria we won’t be able to follow it, and we might even take comfort in our disagreement about moral foundations since it hides our moral ugliness behind a supposed scholarly riddle, i.e. “as soon as we solve this trolley problem our inherent human goodness and moral strength will more than suffice to make everyone do the good!” Faced with the moral vision of myself, imagining my ignorance is more pleasant than admitting my wickedness.
So the present terms of the debate over whether man can be good without God are largely moot: even if our moral code made no reference to God we would need God to be good, because our need for him is not principally in his justification of a law we can follow fine by ourselves but his strengthening of the heart to enjoy the moral law which, in fact, both arises from his action and is ordered to union with him. Again, even if (and I take this as per impossibile) a secular, evolutionary psychology morality were made perfect in every jot and tittle, the primary role it would play in divine providence would be for God to make persons recognize we are insufficient in ourselves and that our sufficiency is in God.