There are two conflicting definitions of patriarchy. The first definition is disproportionate level of male headed households. This is not a real problem for any one. The second definition of a system that is established to benefit men at the expense of women  is hugely problematic.
Male headed households or clans is clearly evident throughout history. This does not make it a bad thing. While men have had more respect and authority throughout most of history, it was not privilege. It was obligation. Men had the obligation to protect their families. To do this the authority to command the family was absolutely essential. Men had the obligation to provide for the family. To do this they authority to make choices about putting himself at risk was absolutely essential. Under this definition of patriarchy women where not oppressed nor where they privileged. Women had very few obligations and very little authority, things where balanced. Men had huge burdens of obligations and very significant authority to meet these obligations. Things where balanced. There was never a system that benefited men at the expense of women.
The term patriarchy is used to describe and explain many very real problems that both men and women face. The problem is that it is not patriarchy. There are two distinct and separate things that are mashed together and called patriarchy. Individually either oligarchy or traditionalism explain everything that is attributed to patriarchy, only better. There is also no implicit or explicit sexism in the terms oligarchy or traditionalism.
Oligarchy is the rule by a few. “Not all men are patriarchs” disproves patriarchy and proves oligarchy. It is not men or fathers that have power, but a select few elite. The requirement to be an oligarch is wealth and power, not gender. It is true that most oligarchs are men, this is not a requirement. There are more than enough examples of female oligarchs to disprove it’s about gender. There have been many female oligarchs from Cleopatra to Queen Elizabeth. The oligarchy does make rules, laws and traditions that perpetuate the oligarchy, expand it’s power and oppress the poor. There is rich oppressing poor, not men oppressing women. It is the powerful creating oppressive systems, not men in general. Men are every bit as oppressed by the Oligarchy as women are. Correctly identifying the problems of Oligarchy as Oligarchy will let us find real solutions.
The other half of “patriarchy” is traditionalism. Traditions dating back to even before the dawn of civilization are the driving factor in gender roles. Traditionalism does not only date back to 1950. To get a good look at traditionalism look at year 195, not 1950. The distinct gender roles for both men and women worked well to ensure the survival of the species. These gender roles are restrictive and abusive to both men and women. Women are sex objects, precious things that need to be locked away for their own good and protection. Men fair no better under traditionalism. Men are success objects. Men are disposable utilities to be used up and discarded like human refuse. These roles worked well to perpetuate the species when food and survival where daily struggles. Perpetuating these roles in the modern world is bad for both men and women. Callously discarding men and infantalizing women does no one any good. Correctly identifying the problems with traditionalism as traditionalism will let us find real solutions.