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Man is more perfect?  I am not sure that is the right statement.  If man was more perfect, then Adam would not have been tempted by Eve.

Pic related from Augustine's Confessions Book 13 chapter 32. My expression may not have been apt, St Augustine does it better.



I think most modern women do not recognise God's order, to quote, "as to the bodily sex she would be subject to the male sex", hence feminism is a rejection of God by rejecting His order. (And also rejecting the order of the House, God/Christ > Husband > Wife > Children)

Adam eating the apple is an interesting thing to think about, since he had a perfect nature and not a fallen one unlike us he surely knew what he was doing, yet he still choose to sin and betray God. So why did he do it? Perhaps he knew that God would save his wife through Christ if he did so? I wouldn't say that Adam sinned with the intention that God would save him because from what I understand the devil and judas both sinned assuming on God's mercy that He would have mercy on them, and this only accelerated satan's fall and solidified judas's damnation as they abused the Divine Mercy. So at least if it was for Eve's sake it would have been more charitable but this cope because you can't do evil to do good. This is just speculation and I don't really know why Adam chose to sin, interesting nevertheless.

What is the difference between quality of nature (which seems to say their equal) and bodily sex (which man has authority over woman)?

I don't know but I presume it has to do with the body, i.e is male and female only qualities of the body and not the soul? So then to say female nature would be referring to the flesh and not the soul, which would make male nature > female nature. 

So both men and women are equal in terms of their soul, being made in the image and likeness of God, which is reason and will (but in the image Augustine calls it the quality of nature, perhaps referring to the rational nature?). But their bodies is where things are unequal, as per the order God has made. I'm not certain on the details maybe some more educated users can chime in.