John Locke lived from 1632 to 1704. So one should not expect him to be free of sexism (or of heterosexism). He assumed that in case of any disagreement, husbands would hold more sway than their wives over their common enterprise of mutual support and of bearing, rearing and providing for children. In Section 82 of his 2d Treatise on Government: “Of Civil Government,” in Chapter VII, "Of Political or Civil Society," John Locke writes:

... it therefore being necessary that the last determination, i. e. the rule, should be placed somewhere; it naturally falls to the man’s share, ...

But he insisted that the authority of husbands extended only to their common enterprise and no further:

... this reaching but to the things of their common interest and property, leaves the wife in the full and free possession of what by contract is her peculiar right, and gives the husband no more power over her life than she has over his; ...

The remainder of the surroundings passage, Section 77-83, points out how big and important the common enterprise of husbands and wives is. He argues in effect that the magnitude of the common enterprise over which John Locke assumes that husbands will have the last determination or rule can create the misunderstanding of a general authority of husbands over wives. 

Besides his denial of any general authority of husbands over wives, John Locke's description of the nature of the "conjugal society" between spouses is of lasting importance. In section 83 he writes:

Conjugal society could subsist and attain its ends without [absolute authority of the husband]; nay, community of goods, and the power over them, mutual assistance and maintenance, and other things belonging to conjugal society, ... that contract which unites man and wife in that society, as far as may consist with procreation, and the bringing up of children till they could shift for themselves; ...

In the quest for equality between men and women, our society has run the risk of underemphasizing the importance of child-rearing. For example, in principle, a duty of staying home to take care of the kids could fall on husbands and wives equally. So there is nothing inherently sexist in believing that one parent should stay home to take care of the kids. But those pushing for greater equality for women have often taken the path of least resistance by arguing that it is OK for both parents to leave the kids in the care of someone else rather than insisting that fathers and mothers on the whole pick up an equal share of child-rearing responsibilities, with the arrangements as much as possible leaning toward at least one parent staying home with the kids. 

One might argue that one could never succeed in getting to a situation in which there are just as many stay-at-home dads and stay-at-home moms. But our society hardly even tries. Stay-at-home dads, like stay-at-home moms, should be praised for making an economic sacrifice for the sake of the next generation, not looked down on.

I suspect that in the case of most families, the positive spillovers to others outside the family from devoting more resources to child-rearing will exceed the loss of positive spillovers to others outside the family that would arise from work outside the home. Whether or not I am right that child-rearing externalities are on average bigger than market-work externalities is an important area for research. At the micro level, in quantifying child-rearing externalities, it is important to realize that, to the considerable extent that children care about themselves more than their parents care about them, that one minus the coefficient of parental altruism times any benefit to kids must be counted as a child-rearing externality. I make my case for the importance of any effect we have on the next generation at the macro level in "That Baby Born in Bethlehem Should Inspire Society to Keep Redeeming Itself."

For links to other John Locke posts, see these John Locke aggregator posts: 

• John Locke's State of Nature and State of War
• On the Achilles Heel of John Locke's Second Treatise: Slavery and Land Ownership 

For reference, here is the full passage from John Locke's 2d Treatise on Government that I am analyzing in this post:

§. 77. GOD having made man such a creature, that in his own judgment, it was not good for him to be alone, put him under strong obligations of necessity, convenience, and inclination to drive him into society, as well as fitted him with understanding and language to continue and enjoy it. The first society was between man and wife, which gave beginning to that between parents and children; to which, in time, that between master and servant came to be added: and though all these might, and commonly did meet together, and make up but one family, wherein the master or mistress of it had some sort of rule proper to a family; each of these, or all together, came short of political society, as we shall see, if we consider the different ends, ties, and bounds of each of these.

  §. 78. Conjugal society is made by a voluntary compact between man and woman; and though it consist chiefly in such a communion and right in one another’s bodies as is necessary to its chief end, procreation; yet it draws with it mutual support and assistance, and a communion of interests too, as necessary not only to unite their care and affection, but also necessary to their common offspring, who have a right to be nourished, and maintained by them till they are able to provide for themselves.

  §. 79. For the end of conjunction between male and female, being not barely procreation, but the continuation of the species; this conjunction betwixt male and female ought to last, even after procreation, so long as is necessary to the nourishment and support of the young ones, who are to be sustained by those that got them, till they are able to shift and provide for themselves. This rule, which the infinite wise maker hath set to the works of his hands, we find the inferior creatures steadily obey. In those viviparous animals which feed on grass, the conjunction between male and female lasts no longer than the very act of copulation; because the teat of the dam being sufficient to nourish the young, till it be able to feed on grass, the male only begets, but concerns not himself for the female or young, to whose sustenance he can contribute nothing. But in beasts of prey the conjunction lasts longer: because the dam not being able well to subsist herself, and nourish her numerous off-spring by her own prey alone, a more laborious, as well as more dangerous way of living, than by feeding on grass, the assistance of the male is necessary to the maintenance of their common family, which cannot subsist till they are able to prey for themselves, but by the joint care of male and female. The same is to be observed in all birds, (except some domestic ones, where plenty of food excuses the cock from feeding, and taking care of the young brood) whose young needing food in the nest, the cock and hen continue mates, till the young are able to use their wing, and provide for themselves.

  §. 80. And herein I think lies the chief, if not the only reason, why the male and female in mankind are tied to a longer conjunction than other creatures, viz. because the female is capable of conceiving, and de facto is commonly with child again, and brings forth to a new birth, long before the former is out of a dependency for support on his parents’ help, and able to shift for himself, and has all the assistance that is due to him from his parents: whereby the father who is bound to take care for those he hath begot, is under an obligation to continue in conjugal society with the same woman longer than other creatures, whose young being able to subsist of themselves, before the time of procreation returns again, the conjugal bond dissolves of itself, and they are at liberty, till Hymen at his usual anniversary season summons them again to choose new mates. Wherein one cannot but admire the wisdom of the great Creator, who having given to man foresight, and an ability to lay up for the future, as well as to supply the present necessity, hath made it necessary, that society of man and wife should be more lasting, than of male and female among other creatures; that so their industry might be encouraged, and their interests better united, to make provision and lay up goods for their common issue, with uncertain mixture, or easy and frequent solutions of conjugal society would mightily disturb.

  §. 81. But though these are ties upon mankind, which make the conjugal bonds more firm and lasting in man, than the other species of animals; yet it would give one reason to enquire, why this compact, where procreation and education are secured, and inheritance taken care for, may not be made determinable, either by consent, or at a certain time, or upon certain conditions, as well as any other voluntary compacts, there being no necessity in the nature of the thing, nor to the ends of it, that it should always be for life; I mean, to such as are under no restraint of any positive law, which ordains all such contracts to be perpetual.

  §. 82. But the husband and wife, though they have but one common concern, yet having different understandings, will unavoidably sometimes have different wills too; it therefore being necessary that the last determination, i. e. the rule, should be placed somewhere; it naturally falls to the man’s share, as the abler and the stronger. But this reaching but to the things of their common interest and property, leaves the wife in the full and free possession of what by contract is her peculiar right, and gives the husband no more power over her life than she has over his; the power of the husband being so far from that of an absolute monarch, that the wife has in many cases a liberty to separate from him, where natural right, or their contract allows it: whether that contract be made by themselves in the state of nature, or by the customs or laws of the country they live in; and the children upon such separation fall to the father or mother’s lot, as such contract does determine.

  §. 83. For all the ends of marriage being to be obtained under politic government, as well as in the state of nature, the civil magistrate doth not abridge the right or power of either naturally necessary to those ends, viz. procreation and mutual support and assistance whilst they are together; but only decides any controversy that may arise between man and wife about them. If it were otherwise, and that absolute sovereignty and power of life and death naturally belonged to the husband, and were necessary to the society between man and wife, there could be no matrimony in any of those countries where the husband is allowed no such absolute authority. But the ends of matrimony requiring no such power in the husband, the condition of conjugal society put it not in him, it being not at all necessary to that state. Conjugal society could subsist and attain its ends without it; nay, community of goods, and the power over them, mutual assistance and maintenance, and other things belonging to conjugal society, might be varied and regulated by that contract which unites man and wife in that society, as far as may consist with procreation, and the bringing up of children till they could shift for themselves; nothing being necessary to any society, that is not necessary to the ends for which it is made.