Women are to submit to their husbands. The man is called the head. It is authority. However, that does not mean men should compel obedience. Submission is freely given, which is why the apostle urges them to do that.
As to Eph. 5:21 it is the summary statement spelled out in the next sections. They are to submit to one another within the context of the roles they find themselves in. Wives submit to husbands, children obey parents, slaves submit to masters, etc. And within that were cautions, husbands love your wives and give yourself up for them, fathers do not exasperate your children, masters do not threaten, etc. The cautions were necessary because they did have authority. But they were not to lord it over the people they had authority over.
Moreover we see it in multiple contexts. We never see the opposite:
Col 3:18 Wives, submit to your husbands, as is fitting in the Lord.
1Pe 3:5 For this is how the holy women who hoped in God used to adorn themselves, by submitting to their own husbands,
Eph 5:24 Now as the church submits to Christ, so also wives should submit in everything to their husbands.
Tit 2:3 Older women likewise are to be reverent in behavior, not slanderers or slaves to much wine. They are to teach what is good,
Tit 2:4 and so train the young women to love their husbands and children,
Tit 2:5 to be self-controlled, pure, working at home, kind, and submissive to their own husbands, that the word of God may not be reviled.
It is strange that you say the exact opposite of what the text says. In the context of sexual relations, where both is to meet the need of the other, they both have authority over the body of the other, in the one flesh relationship:
3 Let the husband render unto the wife due benevolence: and likewise also the wife unto the husband.
4 The wife hath not power of her own body, but the husband: and likewise also the husband hath not power of his own body, but the wife.
5 Defraud ye not one the other, except it be with consent for a time, that ye may give yourselves to fasting and prayer; and come together again, that Satan tempt you not for your incontinency.
In both cases you are ignoring the context. In Ephesians 5:21 the nature of the submission is spelled out in the next sections. In I Corinthians 7 it is clearly in the context of sexuality. And here both have some authority over the other because both have sexual needs, and both have an obligation to try to meet the needs of the other.
In none of these cases should it be compelled. On that we agree. But authority does not cease to be authority because it does not force itself on another.
Jesus put the interest of the church ahead of His own. That in no way means he placed her in authority over himself. He is always Lord. Someone can act sacrificially in love, and still be in authority. A parent who gives his life for his child did not put the child in charge. He put the interest of the child first. The child may be too young to even have a clue what is happening. It is not a matter of authority but of love.