There are some caveats to the whole "submission" thing. If the woman recognizes the truth in Orthodoxy and wants to convert for that reason, then I say well and good. If she converts just because "I'm a man and I say so" ... then the only thing she has demonstrated is her willingness to put what a man says (because he is a man) above her conscience before God. God forbid.
When I was single I was being pursued (diligently!) by a man who was a minister. Presbyterian I think? He would talk over me and insist that what he was saying was true and I was wrong and I must accept his word and affirm it. He was determined that I was going to marry him and we were going to pursue missionary posts in China based out of Australia.
I cut off association with the man.
No one has more authority than Jesus. But we don't see Him steamrolling anyone, and certainly not on the basis of their sex.
(Believe me, I wish for nothing more than to have decent order in my family. My husband is spiritually - conflicted? Under attack? Eventually after some years I could no longer wait for his "leading" when it wasn't coming, and that's when I discovered Orthodoxy. Now unfortunately I cannot betray what I know to be true for the sake of "submitting" to wrong beliefs and such. But fortunately he has a fairly good grasp on most things, and also fortunately my priest was a good guide in ways to promote peace in such circumstances. Our marriage is actually many times exponentially better than it was before I found the Church.)
But a woman's willingness to "submit" to a man if it requires her to betray her beliefs to God is not something to recommend her.
There are 3 persons in a marriage: God, the husband, and the wife.
Husband’s role: love towards sanctification, the responsibility/suffering of leadership, provision for the family, and protection; loving, cherishing, protecting, providing, and honoring the wife.
Wife’s role: trust, submission, and respect
God’s role: revealing the commandments that the husband and wife should “melt” into and abide by for harmony and peace (among other things) of the little church at home... as our God is a god of peace and order, not of chaos and disorder.
The husband is to love like Christ, and the wife is to respect as the Church.
Christ didn’t lead by coercion, but with loving responsibility/suffering without forsaking the commandments of His Father. By doing this, He led humanity on the way, truth, and life of salvation. The husband is to lead how Christ led - for the salvation of the family. This is suffering - and the wife doesn’t go through this kind of suffering because this is not her role.
The wife is in the best place considering they have the role of submission/obedience... oh how many monks have been led to salvation by obedience (the greatest virtue of Christianity). However, if the husband is not living an Orthodox way of life, the wife has the responsibility to respectfully talk to the husband about that. Vice versa, the husband lovingly calls the wife out if she isn’t leading an Orthodox way of life.
Quote by St. Paisios sums this up:
“What is it that most unites husband and wife?”
“Gratitude”, I answered.
“They love each other for what they give as a gift to one another. The wife offers her husband: trust, devotion, obedience. The husband offers his wife: assurance and security that he can protect her. The wife is the noble lady of the household, but also the mature servant. The husband is the captain of the household, but also he is the lowest laborer.”
I could write a whole book on this, but I will refrain from going deeper into this topic as I have gotten my main point across.
Edit: Best Orthodox book on marriage after On Marriage and Family Life by St. John Chrysostom:
https://www.amazon.com/Marriage-Spiritual-Arena-Πνευματικό-Γυμναστήριο/dp/1932455302