Xiao
This is the best description I have found of the benefits of Patriarchy, but beware of its Authoritarian tinge.
"A patrilineal society is one where marriage is permanent, husbands work to provide for the support of the children, and children take their father's surname. Historically, all societies advanced enough to have settled as opposed to nomadic (e.g. slash-and-burn) agriculture and to have iron tools are patrilineal ones with permanent marriage and paternal support for the raising of children.
Matrilineal societies, where children take their mother's surname, are typically primitive ones where there is no marriage but women have transient boyfriends, and children do not know who their father is but only who their mother is. Although boyfriends will bring gifts on the occasions when they want to please the women, men do not support their children, not knowing even who they are. In matrilineal societies women typically support themselves and simultaneously raise their children without much help from the men. The men typically spend their days hunting birds for war feathers, congregating for their war songs and dances, and conducting raids on and carrying on feuds with, neighboring tribes.
With a patrilineal society, men give up a carefree life for a life of toil and responsibility, but in return gain not only the permanent faithfulness of their wives, but also being revered by their children and a sort of immortality in being revered by their descendants. Since the successful yoking of the energies of once carefree but unproductive men to the productive labor and toil with which to support their wives and children is the fundamental precondition to the building of civilization, and this successful yoking is achieved only with the revering of the men by their wives, children and descendants, then it can be said that revering the father is one of the most important things for society.
Thus Confucius is absolutely right: in xiao certainly nothing is greater than revering the father."
Feng Xin-Ming, Commentary on the Xiaojing.