At its core,

[wufwugy]

OTOH, if his argument is that religion can guide morality then I'd say that ship hit an iceberg a long time ago.

The short of his argument is some of what I've mentioned ITT. Religious and mythical archetypes are descriptions of evolutionary adaptation -- primarily through the dominance hierarchy -- that yield the greatest mode of being (morality and behavior) for species survival. For example, the flood myths are about corrupted peoples being destroyed by God, just like how Hurricane Katrina's devastation was due to corruption (everybody knew the levees would break but society was too corrupted to fix them) leading to inevitable destruction by an act of God. The archetypes in religion are such old and biological stories, like how Medusa has a head of snakes that petrifies anybody who sees them, just like how our literal critter ancestors were petrified by literally seeing a literal snake, and perhaps like how the snake of the human soul petrifies that human when confronted.

His argument relevant to postmodernists like Harris and Richard Dawkins is that they think we can discard the moral ideas that have evolved over hundreds of millions of years and instead know what morals are through scientific examination. Peterson argues that science only tells us what is, not how to be; whereas religion and myths are symbiotic in human nature and tell us how to be. An example I like is the idea of sacrifice of oneself for the greater good. This is the core teaching/exemplification of many religions, that the mode of being that is best for the person and best for the society is sacrifice of oneself for the greater good/logos. Science doesn't get humans to that point, but hundred of millions of years of evolution has, and our ideas embedded in our myths and our religion do.