There was a time when the word "Patriarchy" made sense, to describe a pervasive social structure of the Eurosphere.
There was a time when this structure was explicit -- the idea that men were meant to rule both the house and by extension, society and by extension, the world. There was a time when this was widely considered a rational way to organize society, and defended in many a newspaper article and literary essay and public speech. "It's a man's world", they said, men were the smart ones fit to lead society, and blah blah blah.
2nd-wave feminism basically swept that philosophy out of the Eurosphere by demanding an end to the myriad injustices the system created. "Patriarchy" turned from a good word to a bad word pretty quickly, and today you will be hard-pressed to find anyone outside of online forums willing to defend the concept.
And people still use the term to describe the social injustices they face...but the term is no longer useful. Really, It was never useful to describe more than the social structure of the Eurosphere that existed pre-1970s. It described the way people THOUGHT the world worked...but both feminists of the mid-1960s and the people defending patriarchy were missing the point.
See, the trouble with the phrase is that people tend to emphasize the "Patri" part, as if it's specifically the rule of MEN that is the problem. People think that men are the ultimate source of sexism, the source of heteronormativity, and if women were to rule, well that would solve things.
They tend to put less emphasis on the "archy" part -- the idea that someone is ruling someone.
See, there are places on earth where matriarchies exist on the scale of individual families. The Mediterranean Basin is a good example; in places like Italy and Greece, the old mothers are the ones who run households. If you're working with the model so many second-wave feminists used, this family structure is supposed to be a good thing. Women rule the household, not men, and God sees that it is good. No more gender-based injustice. Right?
You wish.
Gore Vidal wrote an essay about the households of southern Italy, where he noted that their matriarchies don't look that much different than patriarchies. He said that the old mothers force their dughters into strict gender-based household roles, as revenge for the same restrictions that were placed on them, in their youth.
The trouble is that the old mothers RULE their households.
Patriarchy or matriarchy, the problem is the Archy.
But still -- there was a time when the Eurosphere could be said to be a general patriarchy. That started to end in the mid-1960s when 2nd-wave feminism took off. Straight women started to complain about the boxes they were being forced into, and started to use the term "patriarchy" to describe their unhappy lives.
Then came the Stonewall riot. Gay people and trans people made a very loud case for their right to exist, and suddenly the issue of gender-related social justice was more complicated then Men Versus Women -- it was also Men Versus Men and Women Versus Women. The war between the sexes was revealed to be a war WITHIN the sexes, with men and women alike taking sides based on supporting tradition or justice.
As a result, the term "patriarchy" lost its use as an explanation of what was going on with gender-based social injustice. Then as now, the term "patriarchy" implied that striaight men, and straight men alone, were deliberately coming down upon everyone out of some kind of inherent evil, that we'd all be happy if mean old Mister Dad was gone --
but if Ms. Mom is just as mean as Mister Dad, where's that coming from? Why would women, who have a subordinate role in "traditonal" Northern European family structures, be supporting such a system? What's the incentive?
The incentive is one that every society faced before industrial agriculture: You Must Make Babies. You must make ten so that five survive. You must have five survive so that your population can grow and survive against its enemies. How a people deals with this incentive influnces the degree to which its members suffer the issues associated with making and raising children; a hunter-gatherer society will have (or keep) fewer kids to avoid outstripping the food supply, whereas an agricultural society will force its members to make lots of kids for the sake of having many farmhands.
What we're dealing with now is the modern effects of that old incentive, filtered through a culture that has been shaped by religion, law, and custom to lock down any attempts to escape the role of Making Babies. Even though the incentive itself was made obsolete by industrial agriculture and scientific medicine, the effects of the old system remain.
We're dealing with the crushing expectations of heteronormativity and cisnormativity. We're dealing with a pervasive social conservatism that forces people into positions and forms that are optimized for making babies. Under this attitude, you are expected to bed only the sex that can make babies with you. You are expected to remain with the type of body that will permit you to make babies, and to accept the pronouns and roles associated with it. if you are by chance born with genetalia that do not permit you to make babies, you are expected to undergo surgery that will create genetalia that resemble the baby-making ones, regardless of the expense and complications of these surgeries. Frequently this surgery will be performed upon you as an infant, without your consent, sometimes without the consent of your parents. In all cases you are expected to get married for the purpose of making children, with adoption considered a second resort for those couples who look like they SHOULD be able to make children, but are unable to. You are not expected or encouraged to consider adoption as a first resort, because you're supposed to be MAKING babies. If you are young and pretty you are expected to welcome the advances of those who would bed you, but ONLY if it is from the sex that would make it possible to have babies with them -- elsewise you're engaging in the destruction of society. You are expected to enjoy the act that usually leads to making babies, and if by chance you're not intersted in the least, fuck you. Who cares what you want? There's babies to be made.
If you believe Gore Vidal's assessment of matriarchies, then the attitude of "shut up, get married and make babies for the motherland" is produced by both Matriarchies and Patriarchies. Both versions of a household stuff their members into pre-made roles that have little to do with the shape of the people being stuffed.
(You can hear Reb Tevye singing "Tradition" in the distance.)
Women suffer more under this social structure for the aspects that involve being forced to carry fetuses to term, as the structure of human biology is QUITE unfair where baby-making is concerned. But everyone, to one extent or another, gets caught up in the giant maelstrom of bullshit that swirls around the issue of Making Babies.
Who exactly is served by this system? The people selling wedding packages? The ones selling baby outfits?
The people who can be said to deliberately supoprt this system -- the ones who write legislation against trans people, against abortion, against civil rights for gay people -- aren't doing it out of the economic incentive for making babies. That's long gone. They're doing it because
TRADITIOOOOON!
(Tradition!)
...
So what do we call this all-pervading expectation?
The term "Kyriarchy" was coined in 1992 to describe the interconnected set of opressions and submissions that people face, more specifically, a social structure built around various opressions. But it hasn't caught on. People don't know what the "Kyri" part means, so it's not nearly as catchy as "patriarchy". And it's not specific to issues if sex and gender, so all we've got is "heteronormativity" and "Cisnormativity" and boy those are a mouthful. And if you choose one of those, you're leaving the other one out in the cold.
"Social Conservatism" is all-encompassing but isn't all that specific.
What about...Amigara Fault?
Like, "This is your hole. It was made for you."
"That looks like it's going to completely re-shape me."
"Yes! Into something that will be more useful to the village. Come on, in you go."