A condemnation of one part of a system isn't necessarily a commendation of its opposite. I constantly encounter men who are offended by criticisms of patriarchal systems of power, to whom I say: your "masculinity" isn't under attack by anything except your insecurities. Perhaps, a matriarchal order is a viable solution to our problems - we haven't tried it before - and we should question why that is. But, a more critical question is: why does the idea of a female-led society scare so many men? And at a fundamental level, I might add.
For the sake of honesty, and before I continue, I also need to add that I was not always immune to that kind of thinking; it took conscious effort to change it.
From what I can see, from the implications in the remarks of the men with whom I've had this conversation before, fear of having women in power is a reflection of guilt. There is deep-seated guilt in some men about how they've treated women and how they will continue to treat them while they hold the social upper hand. Moreover, when you understand you've done something wrong, you know there are consequences. Many men fear the oppression they have perpetuated.
In my dialogues with friends and colleagues, I encounter arguments for the continuation of male-dominated societies that invoke nature and religion. The natural view, which often comes in the form of "it's always been this way," is the most popular contention and easily countered by an appeal to the naturalistic or genetic fallacy. That something has "always been that way" doesn't qualify it as optimal or even good for the current state of humanity.
Evolutionarily, for example, humans engaged in behaviours we now see as heinous. Felines and some primates currently entertain infanticide to preserve their genetic lineage or manage the cost-benefit discrepancies of rearing single-parent offspring. There is good evidence that humans did the same in the distant past. And killing babies is only one example amongst hundreds of how "things that were that way" changed to improve modern society.
And the religious argument is just that, religious. According to the Roman Catholic Church, contraceptives are worse than the AIDS epidemic Africa suffered in the absence of condoms.
Some argue that the relegation of women to the status of second-class citizens has social utility, a mistake that has cost us primarily by increasing poverty and causing overpopulation. The ramifications of keeping half of the human race in a state of inferiority will continue to be detrimental to our progress for decades or centuries—a direct reflection of human stupidity, according to economics. One has to ponder how different it would be if women had complete control of their reproductive systems from the beginning. And I'm not talking about sex, but about making babies that might have had to die to accommodate a caveman's ignorant dispositions or a cavewoman's fear of raising that baby alone. Sadly, even today, the vast majority of single-parent households result from men's lack of accountability.
Others assert that this is the best time for women in history, and while this is true, they ignore that any particular point in history was once the best time for anyone. "Having it good," as people love to say, doesn't preclude the need for improvement. The emancipation of slavery in the United States was once the best possible time for African Americans. Still, we can agree that their experience has improved since January 1 of 1863. Furthermore, we need to recognise that it still needs improvement. When you think about it, we don't have to go back too far to see how we treated autistic people before we decided to understand their condition, and we still have much to know about them and how to be good for them.
Now, the least sophisticated arguments come as personal attacks. References to my masculinity or my political views seem to lessen many a boy's fear when in the presence of strong women. I pity you if you've not stood beside a woman as her equal or if you haven't trusted a woman to be as strong as you are. Worse, if you haven't had a woman give herself to you out of sheer desire and not for the expectation of symbolic rewards, I feel sad for you because you haven't correctly lived.
I'll repeat it, a condemnation of a part of a system is not a commendation of its opposite. Your "masculinity" (notice the quotation marks to indicate the sarcastic value such a word has when referencing your weakness) isn't under attack by anything except your insecurities. The point isn't for women to control you or to treat you the way you've treated them, it's about their chance to be equal to men, and if this still bothers you, that's a you-problem.