The cliched, generic way of the male heading to work, doing construction, making and paying the bills. While the wife stays home and cares for the children, does the dishes, and has adultery with your neighbor. We've all heard the stories and you have too, yes it exists, yes it's common, and furthermore, yes the woman can rule the house too.
Of course, I'm not denying that there are many Eastern countries (e.G. Saudi Arabia) that definitely do live under one, where women are actually treated as being less than their husbands. However, this is the not the same for women living in the first world as we live in a society that already has equal rights for all genders. I'd even go as far to argue that women themselves have more rights than men do these days.
The patriarchy is basically just a way to blame everything that doesn't inherently benefit a woman as being the fault of men. They do this by creating propaganda and false statistics that are spread everywhere and continuously mislead the public. The wage gap is a perfect example of this, when feminists tried to claim that women were being paid less than men just because of the fact that they're women. This is simply untrue, as when you take into account that men are more likely to work overtime, take less days off and take more high risk and more higher-earning jobs, this supposed gap is non-existent. It also gives feminists an excuse to come across as victims because all the men are in power, when in actuality, women have every opportunity to enter those positions in power, they just choose not to. They could change it if they wanted to but they don't, because then they won't have their excuses for misandry and crying out that they'e oppressed.
Basically, there is no first world patriarchy, and men are not inherently out to oppress women; I'm pretty sure they have better things to do.
The term "Patriarchy" is just a boogeyman term used by certain feminist to blame men for their problems. You're a strong woman, you're NOT a victim. The only thing you're doing is alienating men when you use this term. It's degrading to yourself and to men, so knock it off. Instead of complaining about it DO something about it. The law legally protects your equality. Now in 3rd world countries that's another story, so instead of knit-picking in America why don't you focus you're time preaching equality there where it is needed?
While we still live in patriarchal society, much like our the history of the society was formally a matriarchal society. This changed for unknown reasons but nonetheless a change of this is inevitable in the near future, whether this change be to full control or will for the first time in humans and animal history, two sex's will share power.