Summary: Relationships and mutual submission is what brings about freedom rather than captivity.
f you've served in the armed forces you attended a multi-week camp even which was meant to acquaint you with a new way of living your life. This new way of life included, as Sgt. Hulka so elaborately said in the movie Stripes, " I'm gonna teach every last one of you how to eat, sleep, walk, talk, shoot, shit like a United States soldier. Understand?"(1) The amazing thing is that a transformation takes place as a person undergoes basic training. They gain a freedom to do things they never could do before. There is a strength, a connectedness and the like that only happens once they "submit" to the authority over them.
The passages you've heard usually makes women squirm. When women hear, "Wives submit to your husbands" or "the husband is the head of the wife", an iciness often invades a church. It doesn’t need to because, our traditional way of understanding these phrases are usually off base.
Verse 21-22 wraps up what it means to be filled with the spirit. Submitting one to another is the last of five participles. In verse 22 the word "submit" is not in the Greek text. Its use is implied from the previous verse. It is an unfortunate mistake to break the narration of the letter at this point. What Paul does is show how being filled with the Holy Spirit impacts not only our worship but the day-to-day relationships we have.
Paul is again underlining a revolutionary thought for those who follow Jesus. We are not in charge of our live but our lives are subject to others, willingly, sacrificially, and Christ like.
In the first century, Paul's thinking on this was radical. To start consider the fact that he actually "wrote" to the wives who were part of the church. He didn't tell the husbands to inform them. Secondly, Rome was a paranoid place to live. Other religions existed but only as it served Rome. It was just another way they could subjugate a conquered nation. Let it get out of hand, like Judaism in 70AD, and you can find your temple in ruin and your people slaughtered.
Rome didn't believe in bettering one's self. In spite of the movies, a slave remained a slave till they died. There may have been a few that gained freedom but the rarity of the fact is what makes it newsworthy. People had a "place" in the order of things and changing that made people uneasy which was not a healthy thing to do.
What Paul tells us is that God's radical understanding of relationships takes "us" out of the center and puts someone else there. As wives, husbands, children, fathers, slave/ worker and owner /employers it is easy to view the world and our experience as though we were at the center of everything. The truth is God has stripped us out of that place and put other people there. In chapter 4 we read:
2Be completely humble and gentle; be patient, bearing with one another in love. 3Make every effort to keep the unity of the Spirit through the bond of peace. 4There is one body and one Spirit—just as you were called to one hope when you were called— 5one Lord, one faith, one baptism; 6one God and Father of all, who is over all and through all and in all.