Andrew Perriman, no friend to complementation views, has some interesting reasons why some egalitarian arguments fail. Here’s an excerpt:
Head as “source”? Definitely not
In an attempt to deal with the complementarian argument about male headship, egalitarians have sometimes promoted the view that the “head” metaphor in Hellenistic Greek could denote the “source” of something. C.K. Barrett in his commentary on 1 Corinthians claims that Herodotus uses kephalai for the sources of a river: “The heads of the river Tearos supply the best and finest water of all rivers” (A Commentary on The First Epistle to the Corinthians, 248). But this misunderstands how metaphors work. In this context “heads” refers to the beginning of the river, the furthest point upstream. The furthest point of the river is naturally also the location of the source of the river—that’s how rivers work. But this does not mean when used metaphorically “head” generally means “source”. It denotes the furthest or most prominent part of something, and in a limited number of cases that will be the source. But the connotation cannot be carried over into other contexts. Those who argue that “head” signifies “having authority over” make exactly the same mistake.
Be submissive to one another? No, but…
Paul urges the Ephesians not to get drunk, to sing Christian songs, to give thanks for everything, and to submit “to one another out of reverence for Christ”. He then instructs wives to “submit to your own husbands, as to the Lord” (5:22), children to obey their parents (6:1), and servants to obey their earthly masters (6:5). Egalitarians would like to think that Paul is advocating mutual submission, but this seems unlikely. In the three categories of relationship that follow submission or obedience is in one direction only, which suggests that “to one another” means “according to the relationships of inequality that prevail amongst you”. However, I think Paul’s language does push us to ask why such submission is enjoined:
The particular emphasis of verse 21 extends into verse 22, where the omission of the verb indicates quite strongly, I think, that subordination within the household is more an accepted fact than a deliberate objective, and that it is rather the indirect object (‘to their own husbands’) and in particular the manner of subordination (‘as to the Lord’) that are of primary concern to Paul. So his argument is not, ‘Be subordinate rather than equal or independent’ but ‘Be subordinate as to the Lord, rather than resentfully or from some less worthy motive’. He is not teaching them to be subordinate but how to deal with the subordination that society generally expected of them. Norbert Baumert… says, ‘The actual ethical-theological statement of the apostle is probably: “accept the position appropriate to you under the contemporary circumstances”.’[fn]Andrew Perriman, Speaking of Women: Interpreting Paul, 1998, 53.[/fn]
Read the whole thing.