Patriarchy and Matriarchy describe societies in which the dominant roles in a household are overwhelmingly kept by a certain gender.
In the early days of the Roman Republic, the Patriarch of the family held authority over his children even when they were living outside his household. A Patriarch under severe debt could sell his son to slavery to repay that debt.
In this setting the Patriarch had the decision of life and death upon his children. Deformed children could be left outside to die, and their parents would suffer no penalties under the law.
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Therefore the power of the patriarch in a patriarchy would be highest inside his own family unit. He could determine the fate of his children and wife, although according to Roman Law he could not kill or harm his wife unless in a crime of passion (coming home to find her getting porked by someone else, for example, which is still a valid part of law even in modern Italy).
In this thread I'd like to draw parallels to modern society and prove it to be a Matriarchy, if only in this regard. It is the desire of many women, who are undoubtedly feminists, to have complete control over the life and death of their children. They demand the right to terminate and kill their child, the same right given to the Patriarch which was previously discussed. They reserve the right to sell their child into slavery - grooming them to sexual deviancy and selling them to degenerates. In all of these actions, the man is powerless to resist and stop it, in the same way the woman was powerless to resist the actions of her husband, the Patriarch.
Anons are welcomed to add their own examples, expand my own OP, refute my assertions or call me a faggot.