Patriarchy is the theory that men should be the primary bearers of risks. Risk of death or injury, risk of bankruptcy and failure. In marriage the wife shares much of the risk, but even then the risk is disproportioned. If a man dies his family’s prospects will be badly damaged, but they will at least still be alive. If a man fails at business, his whole family shares his poverty, but only a part of his shame.
Basic economic reasoning means that incentivizing risk-taking requires rewards. So patriarchy entails that at least some men will have greater rewards, perhaps economic, perhaps in the form of legal privileges. (Basic economic reasoning also suggests that in more abundant times, the need for specialization in risk-taking will decrease and we may expect more feminism).
Basic biological reasoning suggests that patriarchy is a maximally-efficient mechanism for giving groups an edge over their competition. These biological forces pushing men towards risk-taking and women away from it are powerful enough that evolution has gotten them written into our blood. More than that, nature herself takes more risks with men than with women: there are more extremely bright men than women, but there are also more extremely stupid men than women.
The gospel supports a version of patriarchy. For example, the Proclamation teaches that men are supposed to be the providers, which is to say the economic risk-takers.
Why? Perhaps its just a recognition of the brute biological facts. It would be consistent with the gospel to let heritage and history be major shapers of our being. But perhaps it has something to do with the divine method we see in Paul’s sermon on the Body of Christ, where God seems to prefer that we not all embody all good human traits equally but that they be heightened in one and lessened in another and made available to all through fellowship and fraternity. There is something good and divine both about taking risks and competition and about security and stability. Although men and women both know both these goods, possessing them in disproportion allows them to be more fully expressed than if they were balanced in each sex. Then, through marriage, the goods we know are shared with each other and disciplined to the whole: men have to curtail their risk-taking for the needs of the family and women have to take a chance on a man.