The Lovely One had a few temple thoughts about parallels.

Eve had to leave.  Adam had a choice.  He chose to leave with her.  So Eve was not in a position to out-serve her husband, so to speak, because his very presence with her was an act of service.  The same pattern, applied, is a woman getting pregnant and the man choosing to stick around to protect her.

One parallel is to Christ and the church.  No matter what we do for Him, we are still indebted to Him just for coming down to our fallen world with us.

If ye should serve him with all your whole souls yet ye would be unprofitable servants.

 

Christ and the church lead on to Paul:

Wives, submit yourselves unto your own husbands, as unto the Lord.

23 For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body.

24 Therefore as the church is subject unto Christ, so let the wives be to their own husbands in every thing.

25 Husbands, love your wives, even as Christ also loved the church, and gave himself for it;

Which seems to bring us back to Adam and Eve.

For her, the meaning was that wives should not try to outcompete their husbands in a competition to see who can claim the greatest sacrifice or service. For me, the meaning is still percolating.