Benevolent sexism and the Patriarchy are contradictory, and allows radical feminists to absolve the responsibility of any male inequalities from any pro-woman or feminist agenda.

Patriarchy: "Most forms of feminism characterize patriarchy as an unjust social system that is oppressive to women." "[It] can is a social system in which the role of the male as the primary authority figure is central to social organization, and where fathers hold authority over women, children, and property. It implies the institutions of male rule and privilege, and entails female subordination." -wiki

Benevolent sexism: An easily testable concept that illustrates how some men treat women better than other men. Male only draft, the lifeboat's women and children first, chivalry, etc... Consequentially, Benevolent sexism for one sex is actually Hostile sexism for the other. Women get to board lifeboats, men get to drown. Who is the oppressed group in this picture? Men. Historically, the latter example may have made sense at the expense of the lives of men, but not in the past 100 or so years.

How on earth anyone can hold these two concepts simultaneously and maintain a coherent perspective is baffling. They completely contradict each other. Either you have one, but not the other.

The draft, or traditionally male-only armies, is an example of benevolent sexism... Holding that women are too weak to fight and should stay home and make babies. But, the definition of Patriarchy concludes that women are oppressed and are subordinate to men. Where in the history of mankind has an oppressed group of people been spared being used as cannon fodder? How is forcing or expecting the average man to participate in wars with exorbitantly high casualty rates (up until very recent history) not a form of subordination?

There are other less obvious examples that illustrate the contradictory nature of those two ideas, but the reason why the Patriarchy is nonsense in any regard is that it commits the apex fallacy. The Patriarchy should be defined as:

Is a historically unjust social and political system that is oppressive to everyone except the upper class. It just so happens that most of the power has been and is in the hands of men [and powerful women have been just as menacing as other powerful men]. The social construct has gender roles that see to it that men are the primary protector and laborer of the family, whilst the women, in a mutual relationship, was the primary caregiver and maintained difficult to obtain but sustainable fertility limits for their society. A Patriarchy cleverly maintains that men, oppressed groups, and slaves be used as cannon fodder and laborers, while keeping women in, relative to men, a comfortable environment to reproduce the next generation of soldiers and workers.

In the context of that definition, you could explain how there is a Patriarchy with respect to the draft or male-only armies.

You cannot hold the original definition of the Patriarchy and say that the Patriarchy harms men too. It is completely self-contradictory. Benevolent sexism does harm men, but it and the Patriarchy are mutually exclusive... You can't just highlight examples of how Benevolent sexism harms men and conclude that the Patriarchy harms men.

From Benevolent sexism for women rises Hostile sexism for men, contradicting the original definition of the Patriarchy. If one holds that Benevolent sexism harms men, then only the definitions for Benevolent sexism (and from it the inevitable Hostile sexism) and my simplified and refined definition for the Patriarchy make any sense.

For example, the idiot who violated the law and created an extremely inefficient method of evacuating that sinking cruise ship... Women and children first. That is an example of Benevolent sexism for women, and Hostile sexism for men. The concept of women before men makes sense with my definition of the Patriarchy, but is completely contradictory to the original definition of the Patriarchy. With the original definition, women are the expendable sex.

The historical reality of the average person shows no evidence of the oppression of women, only evidence of the oppression of those below the upper class and their institutions for gender roles that demanded and expected physical sacrifice and their lives at war from men, and care-giving and fertility from women. This idea that female privilege only exists out of Benevolent sexism may sound like a way of off-putting any possible feminist or women responsibilities of male inequality, but out of Benevolent sexism to women there must arise Hostile sexism to men. Ergo, female privilege [....] can be born from Hostile sexism to men.