I know what it says there. Adam’s the head of the family and should have behaved in a responsible manner, but instead he deliberately rebelled.
Did he?
Genesis 3:9 And the Lord God called Adam, and said to him: Where art thou?
10 And he said: I heard thy voice in paradise; and I was afraid, because I was naked, and I hid myself.
11 And he said to him: And who hath told thee that thou wast naked, but that thou hast eaten of the tree whereof I commanded thee that thou shouldst not eat?
12 And Adam said: The woman, whom thou gavest me to be my companion, gave me of the tree, and I did eat.
Was Adam lying when he said he ate it because the woman gave it to him? I don’t think so ... God didn’t call him on it, God immediately turned to question Eve. Adam wasn’t even thinking about eating the forbidden fruit, until Eve gave it to him. In fact, God explicitly condemned Adam for listening to Eve:
Genesis 3:17 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, cursed is the earth in thy work; with labour and toil shalt thou eat thereof all the days of thy life.
That doesn’t look like Adam acting purely on his own conscience. Quite the contrary, it looks like Adam failing to exercise his duty to teach, and instead listening to a bad teacher.
The context of your quote from 1 Timothy is of who should have teaching authority, and St. Paul explicitly assigns that authority to Man. The first time Woman attempted to exercise “teaching authority” over Man, it ended in disaster.
IMO.
YMMV.
IANTP.