Over at Sunshine Mary’s, someone pulled out this tired old canard. I was going to respond there, but it turned into a Latin lesson so I thought I’d put it here.
Men are to submit to their wives sometimes,
21 Submit to one another out of reverence for Christ. — Ephesians 5: 21
Let’s deal with this constant misconception and be done with it, shall we?
Interestingly, though most modern bibles seem to split them into two sections, verses 20 and 21 are a single sentence in the Latin:  Gratias agentes semper pro omnibus in nomine Domini nostri Jesu Christi, Deo et Patri,  subjecti invicem in timore Christi. “Literally: Giving thanks always for all things in the name of our Lord Jesus Christ, to God and Father, be subject to one another in fear (the reverence kind) of Christ.”
In other words, Paul wasn’t talking about marriage yet in that sentence; he was talking about Christians in general. Also, subjecti (literally “be thrown under”) may mean “be subject to,” but it can also mean “be supportive of”. And invicem is an adverb meaning “mutually,” so the common translation of “each other” doesn’t mean he’s talking about two people. He’s not; he’s saying Christians need to place themselves beneath one another mutually.
Now, on to verse 22, where he gets into the details of how this is to be done, starting with wives:
 Mulieres viris suis sicut Domino,  quoniam vir caput est mulieris, sicut et Christus caput est ecclesiae, ipse salvator corporis.  Sed ut ecclesia subjecta est Christo, ita et mulieres viris in omnibus.
A slavishly literal translation is, “Wives to your husbands as to the Lord, because the husband is the head of the wife, as also Christ is head of the church, His body, himself its Savior. But as the Church is subject to Christ, so also wives to their husbands in all things.”
Now the context is much clearer. How are Christians to be subject to each other? Well, wives are to be subject to their husbands as they are to the Lord. Why? Because the husband is the head of the wife. Note that Paul isn’t saying the husband should be the head of the wife; he’s saying he is. There’s no choice about that; he can’t decide to let his wife be the head sometimes. (An interesting note: ut, translated here with “as,” very often has a meaning of “in order that.” So you might translate verse 24 as, “But in order that the Church be subject to Christ…” That would make sense, because when wives stop submitting to their husbands, doesn’t it seem likely that the Church rebelling against Christ will soon follow?)
Now on to what husbands are to do. Note that Paul doesn’t just say, “Men, you do the same.” Or he could have saved ink and used “spouses” in the above verses instead of wives and husbands. But he didn’t; he chose different words altogether, as he does later when he talks to children and slaves. To men, he says:
 Viri, diligite uxores, sicut et Christus dilexit ecclesiam et seipsum tradidit pro ea,
Literally: “Husbands, love your wives, as also Christ loved the Church and gave himself over for her,”
While Paul told women to pattern their marital actions after the Church, he is saying men should pattern theirs after Christ. Instead of subjecti (to submit), he switches to tradere, which means to surrender or devote oneself, and pro, which means “for” in the sense of “on behalf of.” That makes sense, because obviously Christ didn’t surrender himself to the Church (that would have been in the dative, “ei” instead of “pro ea”); he surrendered himself on behalf of the Church. Husbands aren’t called to surrender themselves to their wives; they’re called to surrender themselves for them. Huge difference.
What does all that mean in practice? The Church is to be completely obedient to Christ, following his commandments to the letter. Likewise a wife to her husband (except that she doesn’t have to follow clearly sinful commandments, because Christ doesn’t give those to the Church, of course). Christ loves the Church wholeheartedly and gives His life for her. Husbands are to do the same, sacrificing their time and toil, even their lives if necessary, to provide for the needs and ultimately the salvation of their wives. (Note I didn’t say anything about the “wants” of their wives; Christ gives His Church what she needs, not what she wants.)
By this point, it should be clear from the context that this is only “mutual” in the sense that husbands and wives are called to do things for each other’s mutual benefit, because all Christians are called to sacrifice for others, and marriage doesn’t exempt you from that. But the specifics of how husbands and wives are to sacrifice for each other are very different. If you say men submit to their wives, you’re saying Christ submits to the Church. That just doesn’t make sense, unless you redefine “submit” to mean something other than what it means. Christ commands and loves the Church; the Church obeys and beseeches Christ. Never the other way around.