I'd like to say it again, to the less secure giving over authority to another is equivalent to repudiating one's own authority, and so it must be held with white knuckled tenacity.
The transgression(s) in the garden were usurping and repudiating authority, both criminal trespasses the received the sentence of routine domination of Eve for usurping Adam's authority, so that she might learn the proper skills of consultation and deference perhaps, and resistance of everything including the kitchen sink for Adam's repudiation of his sensibilities, so that he might learn the proper skills of conflict management and assertion, not necessarily total dominance, as each did have right to otherwise legitimate authority.
However, the proper balance is restored in Christ. And, it is not so much total submission for Eve that is the answer but the discernment to know when submission is warranted, and for Adam, the discernment to know when repudiation isn't. This discernment is provided in Christ.
'Giving' over authority to another does not necessitate repudiating one's own authority, as usurping authority does 'take' it from another.