Not to derail the thread, but since you invoked the word "submit," let me educate you on the other side of that coin. As you mentioned, men lead their wives. Also notice that wives are rulers, or literally "despots" of the home. The bolded word is only found in the Bible this one time, and it where we get the word "despot" from.
I Timothy 5:14, "Therefore, I want younger widows to get married, bear children,
keep house, and give the enemy no occasion for reproach;"
Oikodespoteo:
- to be master (or head) of a house
- to rule a household, manage family affairs