Well, you are subordinating the woman in the first instance
Sure.

But where does “subordination” mean inferiority?
OK, you agree that they are being subordinated. Where does it mean inferiority? Let’s look as some definitions:
sub•or•di•nate adj.
- Belonging to a lower or inferior class or rank; secondary.
- Subject to the authority or control of another.
n.
One that is subordinate.
sub•or•di•nat•ed, sub•or•di•nat•ing, sub•or•di•nates
- To put in a lower or inferior rank or class.
- To make subservient; subdue.
Those are pretty much the common usages of the word that any reasonable person would use. I don’t think that I need comment further on that.
Do you have to promise to obey your husband as a Catholic? And that he doesn’t have to obey you?
How many quotes from the bible would you need?
Ephesians 5:22: “Wives, be subordinate to their husbands as to the Lord.
St. Paul: “the head of every man is Christ, the head of a woman is her husband, and the head of Christ is God. Man is the image and glory of God, but woman is the glory of man. For man was not made from woman, but woman from man. Neither was man created for woman, but woman for man.” (1 Corinthians 11:7-10)
St. Peter: “be submissive to your husbands, so that some, though they do not obey the word, may be won without a word by the behavior of their wives, when they see your reverent and chaste behavior.”
How about some quotes from Popes:
Pope Pius XI: False liberty and unnatural equality [in authority] with the husband is to the detriment of the woman herself.
Encyclical of Pope Leo XIII on Christian marriage: The man is the ruler of the family, and the head of the woman; but because she is flesh of his flesh and bone of his bone, let her be subject and obedient to the man…
So to be a good wife, you have to submit. And being submissive means:
Definition: 1. allowing others to have control over you; 2. willing to submit to the wishes of others.
Synonyms: compliant, acquiescent, docile, meek, obedient, passive, servile
Antonyms: domineering, controlling, oppressive
Tips: Submissive is derived from the Latin submissio, which means “lowering, yielding.” Picture someone yielding control to someone else. Submissive is generally used to describe people who allow others to control their lives.
Usage Examples:
The submissive woman let her overbearing husband control her. (docile, meek, passive)
The submissive servant did exactly what he was told. (obedient, compliant)
Because she had a submissive personality, she always went along with what others wanted to do. (passive, docile, compliant)
I don’t like her submissive manner, and I sometimes wish she would just stand up for herself. (meek, servile, acquiescent)
If women are not to be submissive, then why is there a discussion about it. Just state that it’s not a requirement and that any statements to the contrary are out of date and no longer applicable to the church today.