If the Great Mother represent Chaos and the Unknown, as both threat and opportunity, the Great Father represents Order and the Known.
As with the Great Mother, the Great Father is a bivalent symbol. Positively, the Great Father represents structure and order. These are vital and adaptive accomplishments, personally and collectively. We need structure for both safety and security. We need norms and habits to regulate our lives.
And yet, if order and structure becomes totalizing the effect can be stifling, stultifying, and repressive. The Great Father can be a benevolent protector or a dominating tyrant.
As Peterson summarizes,
Construction of culture is creation of the mythic Great and Terrible Father, tyrant and wise king, as intermediary between the vulnerable individual and the overwhelming natural world...The wise king maintains stability...The Great Father as tyrant destroys what he once was and undermines what he still depends upon...He is the personification of the authoritarian and totalitarian state...The Great Father is protection and necessary aid to growth, but absolute identification with his personality and force ultimately destroys the spirit.
Again, structure and order provide necessary protections, but too much structure becomes oppressive. This basically mirrors what we observed with the Great Mother. Too much novelty and disruption leads to chaos, but we need to venture into the unknown to expand horizons and possibilities. Simplifying and combining the lessons from both archetypes, we're always balancing between Order and Chaos. This Order/Chaos balancing is a big theme in Peterson's thought. We need the right balance between Predictability versus Opportunity or Safety versus Risk to solve the challenges of life.
Returning to the bivalent nature of the Great Father, we see examples of this in Christianity. We call God our Father, and images of that father can range from the comforting and protective to the judgmental and tyrannical. We also vary in the degree to which we experience God's "rules" as liberating or oppressive. God as Father is a very bivalent symbol in the Christian experience, and not everyone is on the same page. In my experience, in walking alongside ex-evangelicals, a large part of their conservative, evangelical experience was that God, as the Great Father, had become the tyrant. Consequently, movement toward viewing God as kind, wise, protective, caring and benevolent is an important part of their faith development.