Quoting it one last time:
"For all the temptations of native life, one of the most compelling might have been its fundamental egalitarianism. Personal property was usually limited to whatever could be transported by horse or on foot, so gross inequalities of wealth were difficult to accumulate. Successful hunters and warriors could support multiple wives, but unlike modern society, those advantages were generally not passed on through the generations. Social status came through hunting and war, which all men had access to, and women had far more autonomy and sexual freedom—and bore fewer children—than women in white society."
This is what egalitarianism means - everyone had pretty equal access to opportunity and although that access was differentiated by gender, there was no significant social or wealth stratification, no artificial barriers to opportunity to make your way, no traditional power that was maintained at the expense of others through violence (which is what a patriarchy is - because as I know Elle said about 75 different times, it's a dominance based hierarchy and not just a power differential between men and women.) Native cultures were not a patriarchy by any stretch. As it says further down, women held significant political, social and economic power and matrillineal descent was often practiced.
"But, from the Native American perspective, women’s roles reflected their own cultural emphases on reciprocity, balance, and autonomy. Most scholars agree that Native American women at the time of contact with Europeans had more authority and autonomy than did European women."
Men were generally responsible for hunting, warfare, and interacting with outsiders, therefore they had more visible, public roles. Women, on the other hand, managed the internal operations of the community. They usually owned the family’s housing and household goods, engaged in agricultural food production and gathering of foodstuffs, and reared the children. Because women’s activities were central to the community’s welfare, they also held important political, social, and economic power. In many North American societies, clan membership and material goods descended through women. For example, the Five (later Six) Nations of the Iroquois Confederation all practiced matrilineal descent. Clan matrons selected men to serve as their chiefs, and they deposed chiefs with whom they were dissatisfied. Women’s life-giving roles also played a part in their political and social authority. In Native American creation stories, it was often the woman who created life, through giving birth to children, or through the use of their own bodies to create the earth, from which plants and animals emerged."
"Some scholars argue that, after contact, women’s authority steadily declined because of cultural assimilation. Euro-American men insisted on dealing with Indian men in trade negotiations, and ministers demanded that Indians follow the Christian modes of partriarchy and gendered division of labor that made men farmers and women housekeepers. However, other scholars, such as SUNY Fredonia anthropologist Joy Bilharz and University of North Carolina historian Theda Perdue, argue that many indigenous women maintained authority within their communities. Matrilineal inheritance of clan identity remained important parts of many cultures long after contact, and women continued to use their maternal authority to influence political decisions within and outside of their own nations."
https://teachinghistory.org/history-content/ask-a-historian/23931
And, I'm really tired of this, so this is the end of the line for me.