Historically, most societies have been patriarchal, agreeing that a man rightly has rule over his family, which includes being in authority over his wife; and this not merely in the sense of primus inter pares; rather, a wife is subordinate to her husband. This contradicts both egalitarian feminism, which denies male headship, and complementarianism, which allows a sort of authority to husbands but interprets this as the authority of a first-among-equals.
Abandoning patriarchalism was a mistake. Women are in fact inferior to their husbands. This is not demeaning to women any more than it is demeaning to a lieutenant to be inferior to a general. In defense of this I propound three arguments: two from Scripture, and a third from the consensus gentium.
First Argument: Wifely submission is the submission of an inferior.
The sum of my first argument is that the Scriptural requirement of wifely submission is an implicit confirmation of a husband's superiority. Why do I say this? Is is because I think the mere word "submission" implies inferiority, as if it is impossible to submit to a first-among-equals? No. I allow that there are different varieties of submission. In some contexts telling someone to "submit" would not imply that the one being submitted to is a superior. But in other contexts it would imply that. Submission does not always and everywhere imply inferiority. However, the two notions are not just accidentally associated. Submission is among the essential duties (along with such things as honor & deference) that inferiors owe to superiors. Such duties define what it means to be a subordinate; they constitute the nature and quiddity of social inferiority. Because of this, when one who is in fact inferior is instructed to submit to a superior, it is to be presumed that the submission being talked about is the very sort owed by an inferior to a superior as such, and not some lesser sort of submission. To be sure, a lesser degree of submission may be appropriate toward one who is only a first-among-equals; nevertheless, we are probably not talking about that lesser degree of submission when we tell an inferior to submit to his superior.
The same holds when submission is urged upon someone falsely believed, in a society, to be inferior: those who urge this are presumably talking about the kind of submission that inferiors owe to superiors (they just happen to be wrong in thinking that that kind of submission is owed in this case). Regardless of whether the society's belief is right or wrong, what matters when it comes to determining what kind of submission is presumably being talked about is what is generally believed in that society.
I say "presumably" because, of course, a presumption can be overcome: if an author indicates that he rejects society's attribution of inferiority to those being told to submit, the presumptive interpretation would be undercut. But where he does not, the presumption stands. Not everyone agrees with what society thinks. But in general people do. That's what makes it the general belief of that society. So unless an author tells us otherwise, it is reasonable to expect the meaning of his statements to align with how they would generally be understood in his society.
Accordingly, I argue as follows: