Singing the word of God and that which is inspired from the Word of God, it is this action that helps us to submit to one another!

The Word of God reminds me of what the Lord has done.  It reveals imperfections and uncovers promises.  The Word of God brings peace and shows the reality and result of actions.  That is the Word of God.

But the Psalms, there is something unique about the Psalms.  They are full of history, burdens, repentance, and prayer.  The psalms cover the breadth of God, his acts, his mercies, his love, his suffering, his provision, and much more are all found in the Psalms.  Could it be by rehearsing these in our hearts submission to each other would be made easy or at least become more palatable?  Could that be the message (or clue) that Paul is giving the Church?

When we focus on God, what he has done and sing in our hearts about his goodness and the knowledge of His love and protection, submitting is something to be handled under the knowledge of the Word of God.