Let's go with the Wiki definition of Patriarchy (there is probably a billion other definitions):
Patriarchy is a social system in which men hold primary power and predominate in roles of political leadership, moral authority, social privilege and control of property.
And this doesn't exist at the very least in the western world:
Political power - Women have the same voting power as men, so this doesn't apply. Women are the ones voting in the male politicians.
Moral authority - This runs counter to women raising kids and are primarily teachers. At best you can argue it only applies to religions but those don't have as many followers nowdays.
Social privilage - Women have more social privilage, you need to be retarded to debate that.
Control of property - Also doesn't exist in the last century as women are able to have property the same as men.
So yeah, patriarchy doesn't exist unless you go to shitholes or try to make a very specific definition that ignores every rights women have and every duties men have.
So why does patriarchy exist as a term? Because it's the ultimate shifting of goal posts. In the past feminism tried to argue that women are held back by being disadvantaged rights-wise. But those rights were changed for several decades now, yet women are still a minority in STEM, politics and businesses. So to explain that fact in a way that doesn't admit to basic mentality difference between genders, feminists instead argue that society is at fault and need to be changed, and the fault is this "patriarchy" - a boogieman that can be whatever they want it to be. How can the world overcome the patriarchy? By giving control of society to feminists. Which is a win-win, either feminists have an eternal boogieman that they can bitch at, or they get more political power to mandate changes such as diversity quotas.