It boils down to a simple fact: men have dominated human society for millions of years, based solely on the perceived notion that they are the stronger of the binary genders, a notion conceived and reinforced through the application of wholly artificial standards and practices developed to stack the deck in their favor. In the distant mists of the human past, when survival was not assured and no mean feat, men perhaps thought that their hunting and fighting skills made them the natural leaders of humanity. A few million years later, it's easy to see why this idea is wrong...
Looked at from a purely biological and evolutionary standpoint, of the binary genders, women are far stronger than men. You might wish to scoff, since men are clearly bigger, stronger, and faster -- on average -- than women, and you can point the to the differences in sports that both genders compete in as showing that unequivocally, but that is just the kind of artificial selective device that allows men to continue to assert their dominance. If you eliminate artificial distinctions, the picture changes drastically.
First, we have to note that the primary difference between men and women (and I speak solely here of the natural biological genders) is in reproductive capacity. Body physiology between the sexes is identical save where reproductive function is concerned. Both sexes contain the same basic organs, the same neural physiology, the same brain capacity, the same bodily systems... only in the matter of reproduction is there a gross differentiation between the sexes, and if looked at clinically, we note that the demands of allowing a fetus to develop in a self-contained but symbiotic environment coupled with the radical alteration of the physical form required to expel the fetus at the end of gestation and thereby give birth to a child, requires extra reserves of physical strength, endurance, and pain moderation that are not found in men. In essence, the ability to give birth requires that the woman be built in a far more rugged and structurally flexible fashion than men.
Given the input of energy and nutrients required to perform gestation, and constant need to maintain the reproductive system when it is not in use, women had to develop differently in terms of mental frames of reference. For a woman, bodily integrity, access to resources, the need to enjoin the cooperation of others, and recognizing bodily changes as signs of the fertility cycle without outside aid (medicine and health care), caused women to have a far more differentiated mental schema than men. Survival meant having the ability to see the widest range of options possible, to understand and cope with environmental changes that might threaten their existence, and to be able to handle the many and varied tasks required for survival of themselves and their offspring. This put them far ahead of men in the capacity to plan and to adapt.
You may not wish to agree with my characterizations of the biological development of women, but one has to remember the most salient point behind all these things: the survival of the woman was paramount to the survival of the species. Women, the only sex capable of bearing progeny, were a precious resource. It is safe to say that this simple realization drove the creation of the male-dominated, misogynistic societies in the early eras of human history. Men placed women on a pedestal, not because they needed to be, but because that's how men wanted it. The primitive reptilian reproductive drive, coupled to the burgeoning but still primitive human cerebrum, led men to assume that their purpose was to protect and nurture women, to ensure they could continue to reproduce. From that undeveloped thought process, began a long, tortuous journey toward the pedantic, male-dominated world we see today, which persists despite the advance in power of the human cerebrum and the ability of it to override completely, those primitive biological imperatives.
So men, ensconced in their new found role as hunter, fighter, provider, and protector, began to be shaped by this primeval drive. As with anything in the world of natural selection, a series of environmental changes, coupled with societal changes and the continued will to reproduce, pushed the male side of the human species to develop along the lines of its assumed role, and in the process, develop human society concurrently with a male-centered bias. Men considered themselves arbiters of what was best for the whole of human society, and that determination was that women must take a background role, as their ability to drive procreation made them too valuable to allow into the rough-and-tumble of daily life, even as survival got easier and humanity began to flourish.
Women, however, were not content to remain on the sidelines, and we see in every recorded human era, attempts by women to subvert a society that had clearly relegated them to second-class status. At every turn, women proved themselves as capable -- if not more so -- as men in dealing with daily survival, politics, culture, famine, war, disease, and so on. Women continued to agitate for society to accept them in their proper place as equals, even when they had attained such exulted status as empress or queen. Despite the evidence before their eyes, men continued to deny that women could be equal to them, and so even where women made inroads into male-dominated society, those inroads still did not lead to significant change in human society's view of the male-female paradigm. Several million years of natural selection had inured men to the role of women that they had decreed.
Flash forward to the 21st Century, the dawn of the Digital Information Age, where surely, given all that we know, all that we have learned, all the history written behind us, the paradigm has changed? Yet we see that the appearance of change is not the same as change itself. Women, starting in the late 1800s, made significant progress in bringing about seismic scale shifts in society, but those shifts, even leading up to the Women's Suffrage movement and then to the Women's Liberation movement, only scratched the surface of society. The freedom that came with the vote, with the sexual revolution, with the admittance of women into the military -- these things, on the surface, led many to believe that a corner had be turned, similar to that of the end of Jim Crow laws and the birth of the Civil Rights movement. But as we see now, much of what was accomplished was merely window-dressing, because though word of law might have brought forth new liberty and freedom for women, it certainly did nothing to address the creeping and crippling drag of misogyny that lay below the surface. Men did not simply fall prostrate on the ground in their wrongness.
All this said, I am willing to posit that of the genders, it is safe to say that women are stronger than men, for the simple reason that over millions of years, through countless generations, by any and all means at their disposal, on the wrong end of politics and religion most times, disregarded and laughed at, subject to depredation, degradation, and abuse on a constant basis, and even now, having to face misogyny and bigotry almost constantly thrown in their faces, women have doggedly taken everything thrown at their gender and have kept on fighting, kept on hoping, kept on striving. Though at moments they may despair, when it seems men are determined to cast them back into the home, back into roles they have fought to escape from, they rise up and fight. They fight men. They fight their own. They stand silently and endure torture; the stand proudly and shout their refusal to give in. They do not quit. They do not cease. They may grow quiet, but that is only because they are preparing to take up arms once again. Given all that women have suffered at the hands of men and the societies that men have driven, only the strongest could pick themselves up from the ground and continue to press on. That is strength. That is woman.