Partus sequitur ventrum or the American legal concept passed in Virginia in 1662 that the slave status of one's mother determined the child's slave status, rather than say being sired by Thomas Jefferson or other white, non-slave father.
In this original Article I touch on the idea of how marriage might put the man in the driver's seat, in an "ownership" capacity over his wife, the mother, and her children as a way of gaining control over men, thus facilitating the extraction of maximal labor from said men, and also serving in the military. Both of these are the way of showing responsibility for one's legally bound wife and family, but also a way, in the case of the military, of escaping same (through death, getting a free ticket to elsewhere from the government, becoming an errand-boy of the government, etc.).
If women "own" their children (at least through their minority), however, men are reduced to "pollinators" with no need for permanent or, more importantly, documentable, attachment to the women whose children they sire. So in this sense the legal subjugation of women to husbands and other institutions has the major effect of subjugating the men to the government, the church, and to the tax man. You're married to a certain woman, so you'd better be around her constantly, failing some really good (approved) excuse (like being in the military...hmmmm...or off making money), and so she'd better keep having babies or you're in trouble, and you'd better provide for the babies, or you're in trouble, and all this requires a permanent address for when the government comes 'round to press you into some kind of works gang or draft you (or your sons) into the military....and again, you (Mr. Man) had better be there...with the little wifey.
Oh, yeah, and you'd better be married by a certain age or....well, look out! For all the above reasons.
If women are in charge, like, there are "walking marriages" or whatever, where men hold no rights to any children born of women they sleep with, and they don't "marry" them in any official capacity such that any sprogs the woman has "belongs" to or "is the responsibility of" some man (1), then women obviously do what they need to to provide for their children, and they try to limit the number of kids they have so that they can do this more easily. Even if you have some "partner" who is off working full time to pull down dosh to support you and your brood, having one kid after another for years on end and having to look after them is a hassle (and that's taking into account that after about four kids the oldest actually starts helping with the baby-making factory...but still).
So women, left to their own devices, will tend to do the exact opposite of what governments and churches want them to do, i.e., moderate the number of kids they have, in number and spacing of births, and balance making money to support their children and actually raising said children.
And they don't really care what the men do, including almost nothing, so long as they're around for fertilization time, which is never, ever, ever a problem....funny that. We take that one for granted, but....hmmmm....funny that. There's something in there....but...more will be revealed later.
Governments and churches like people to work their asses off and to go off and kill other people that the churches and governments don't like at the drop of a hat. Women might be better at all that stuff (2), but they're also the only ones who can make more babies, and so we don't want them to either get too distracted from the baby-making or get killed doing something stupid like invading a neighboring country.
So it falls to men. If we tell men that the greatest thing is to get assigned a woman for his very own (3), and to get babies off her which will then belong to him, too, and that in exchange for this boon he has to make money, serve God and country, and support this woman and her brood, and the more money he makes and the better his kids do, then the better dad and husband and therefore person he is, what do they do?
And how do we feel about infidelity, smut, porn, unmarried women (or men), neglected children, unemployment, and so on, given that strategy?
(1) Don't let's forget that being "married" to a woman means that any kids she has during the period of the marriage are your children, no matter how sure you are that she got knocked up by somebody else. In Japan, even, a woman has to wait 9 months before getting remarried, while a man may do so immediately. Sexist, yes, but woman can have children and men cannot, so it's a valid distinction...I think so, right?