Neither Male nor Female
Galatians 3:28 in no way abolishes gender distinctions, but rather, the false assumptions that value or worth could somehow be attached to the simple identification of an individual as a slave, free man, Jew, Gentile, male, or female. (After all, if it really did abolish gender distinctions, then how could homosexuality be wrong?) Rather, the text says that in Christ, all were purchased at the same price (the context of the book is obviously justification), and in creation all were equally made in the image of God (Gen. 1:27).
Mutual submission, as presented by egalitarians (so as to abolish the existence of an authority within a relationship), does not fit with the flow of Paul’s argument in Eph. 5 (wives to husbands, children to parents, slaves to masters). Moreover, it does not fit with the established meaning of hypotassō which is always indicative of submission to an authority. The use of allēlous (“one another”) does not necessarily convey the idea of “everyone to everyone” in its common usage. Although it sometimes can indicate this (cf. Mark 9:50; John 13:34; Phil. 2:3), full reciprocity is sometimes obviously not even possibly in view (cf. Matt. 24:10; Luke 2:15; 12:1; 24:32; 1 Cor. 11:33; Gal. 6:2; Rev. 6:4; etc.). In light of the particularly odd construction (“submit unilaterally to one in authority to one another”) it must be deemed best to allow the context (the ellipsis in the original undisputedly indicates a continuation of thought from 5:21 to 5:22) to determine exactly what Paul means. Given the explanation and examples that follow, the best understanding of hypotassō allēlous is “be subject to others in the church who are in positions of authority over you.” In other words, even though you are all one in Christ, do not use this as an excuse to forsake all authority relationships (which are shown elsewhere to be established by God; cf. Rom. 13:1-7), but continue to submit to one another, where authority relationships exist. This is the best meaning linguistically, since it stays the closest to the invariably attested meaning of hypotassō and the contextually interpreted allēlous. It is also the best option contextually because it moves best with the flow of thought in Eph. 5, moving from the whole corporate body to specific application in the home life.
Furthermore, if the idea of mutual submission was the original intent of Paul, then it must also be applied to Christ and the church (Paul’s own divinely inspired illustration). This is a concept that is never attested to anywhere in the Bible and seems illogical at best and blasphemous at worst.
It is also notable that in the explanations of authority relationships that follow Eph. 5:21, Paul takes care to indicate how, in each relationship, the one in authority is to carry out that authority properly, in a God-glorifying manner. The husband loves his wife (vv 25-33), the father does not provoke his children (6:4), and the master desists from threatening and remembers that he too has a master (6:9). This is further proof that Paul clearly has in mind relationships with a source of unilateral authority and does not desire the abolition of those authority structures.
The idea of mutual submission overruling a wife’s submission to her husband as one in an authority position is also inconsistent with other instructions on ordering the NT home (Col. 3:18; Titus 2:5; 1 Pet. 3:1). None of the other passages which carry such instructions for the authority of the husband include any statement that would even vaguely suggest “mutual submission.” Moreover, writing to the culture that he was, Paul would not have needed to tell the wife to submit to the husband (if mutual submission was his intent), but rather, he would have had to make it very clear that the husband was now to submit to the wife. “Husbands submit to your wives” would have been the newest revelation and is what would have needed clarifying and emphasizing. Nowhere in Scripture is such a statement even hinted at. Nevertheless, the commands for wives to submit to husbands are multiple. The classical complementarian position is established therefore by allowing Scripture to interpret itself (as Eph. 5:22ff; 1 Cor. 11:3; Col. 3:18; Titus 2:5; 1 Pet. 3:1 all clarify Paul’s meaning in Eph. 5:21). This is much preferred over the egalitarian argument which pits a false Greek construction of Eph. 5:21 over against the rest of the NT teaching on husband-wife relationships.