St. John Chrysostom writes that Eve mad bad use of her equality with Adam and therefore God made her subject to her husband:
If it be asked, what has this to do with women of the present day? It shows that the male sex enjoyed the higher honor. Man was first formed; and elsewhere he shows their superiority. “Neither was the man created for the woman, but the woman for the man.” 1 Corinthians 11:9 Why then does he say this? He wishes the man to have the preeminence in every way; both for the reason given above, he means, let him have precedence, and on account of what occurred afterwards. For the woman taught the man once, and made him guilty of disobedience, and wrought our ruin. Therefore because she made a bad use of her power over the man, or rather her equality with him, God made her subject to her husband. “Your desire shall be to your husband?” Genesis 3:16 This had not been said to her before.
But how was Adam not deceived? If he was not deceived, he did not then transgress? Attend carefully. The woman said, “The serpent beguiled me.” But the man did not say, The woman deceived me, but, “she gave me of the tree, and I did eat.” Now it is not the same thing to be deceived by a fellow-creature, one of the same kind, as by an inferior and subordinate animal. This is truly to be deceived. Compared therefore with the woman, he is spoken of as “not deceived.” For she was beguiled by an inferior and subject, he by an equal. Again, it is not said of the man, that he “saw the tree was good for food,” but of the woman, and that she “did eat, and gave it to her husband”: so that he transgressed, not captivated by appetite, but merely from the persuasion of his wife. The woman taught once, and ruined all. On this account therefore he says, let her not teach. But what is it to other women, that she suffered this? It certainly concerns them; for the sex is weak and fickle, and he is speaking of the sex collectively. For he says not Eve, but “the woman,” which is the common name of the whole sex, not her proper name.
newadvent.org/fathers/230609.htm
New American Bible (NABRE)
1 Timothy 2:11-14
11 A woman must receive instruction silently and under complete control. 12 I do not permit a woman to teach or to have authority over a man. She must be quiet.13 For Adam was formed first, then Eve. 14 Further, Adam was not deceived, but the woman was deceived and transgressed.
Adam was commanded:
Gen 2:
[16] And he commanded him, saying: Of every tree of paradise thou shalt eat: [17] But of the tree of knowledge of good and evil, thou shalt not eat. For in what day soever thou shalt eat of it, thou shalt die the death.
Eve knew what was commanded:
Gen 3:
[2] And the woman answered him, saying: Of the fruit of the trees that are in paradise we do eat: [3] But of the fruit of the tree which is in the midst of paradise, God hath commanded us that we should not eat; and that we should not touch it, lest perhaps we die. [4]
The judgment:
[14] And the Lord God said to the serpent: Because thou hast done this thing, thou art cursed …
[16] To the woman also he said: I will multiply thy sorrows, and thy conceptions …
[17] And to Adam he said: Because thou hast hearkened to the voice of thy wife, and hast eaten of the tree, whereof I commanded thee that thou shouldst not eat, …