[1006] Eve is the mother of everyone living in Mark2 adamic or non adamic flesh. She is the high priestess of Mark2 human flesh. Just as the Holy Spirit, the heavenly woman, the Jerusalem above of Galatians4, heavenly Eve, is the mother of all angelic bodies

KJV     And Adam called his wife's name Eve; because she was the mother of all living. (KJV)
ASV   And the man called his wife's name Eve; because she was the mother of all living.
GLT   And the man called the name of his wife, Eve; because she became the mother of all living.
YLT   And the man calleth his wife's name Eve: for she hath been mother of all living.
NWT   After this Adam called his wife's name Eve, because she had to become the mother of everyone living (Genesis 3:20).

WLCi·· ar"q.YIw: ~d"a'h' ~ve ATv.ai hW"x; yKi awhi ht'y*h' ~ae yx'-lK' (WLC)
vayikra haadam shem ishto hhava ki hiv hayeta em kol-hhai: (Trans)
ar"q' + w* ~d"a' + h; ~ve hV'ai hW"x; yKi ayhi Hy"h' ~ae yx; + lKO (WLCs)
ar"q' + w* ~d"a' + h; ~ve hV'ai hW"x; yKi ayhi Hy"h' ~ae yx; + lKO (WLCr)
vqw3ms+c ncmsa+a ncmsc 3ms+ncfsc np--- c r3fs vqe3fs ncfsc amsa+ncmsc (WLCp)
WLCi·· and + he called the + Man name of woman of + him Eve because/that/if she herself she has become mother of all of + living (WLCf)

Eve was to become the mother of everone living as distinct from Adam who was the father of Abel. But not the father of Cain, who originated with the wicked one (1 John 3:12). For the power play from Satan was to replace Adam with himself. So he impregnated Eve, whilst she and Satan were still lviing judicially to create a living seed for himself. Then he killed Eve and persuaded her to kill Adam. So that no competing living seed could follow his. That way Satan would become the progenitor of the human race rather than Adam. This is precsiely the sort of thing that lions do to ensure that children do not attack them when they become slightly too old to win a fight. Cain was the liviing seed of Satan and Eve. Then the demons came down and had children with all the earthly women they chose. These were the Nephilim in those days before the flood and after that after the flood. So there were and are many demonic fathers to the human race competing with Adam. But there is only one mother to the Mark2 race and that is Eve.

Gen 6:2 And they saw sons of the Elohim namely daughters of the Man because/that/if good themselves and they took to/for/by them women from all whom they have chosen
Gen 6:3 And he said Jehovah not he is to judge spirit of me in/at/by the Man to/for/by hidden time in/at/by that also he himself flesh and they are going to be days of him 100 and 20 year
Gen 6:4 The Nephilim s they have been in/at/by the earth in/at/by the days those and also after as thus which they are to come in sons of the Elohim towards daughters of the Man and they are going to bring forth to/for/by them they themselves the mighty which from hidden time men of the name 80 (LWTi)

However if she was the only mother then mankind was built upon incest between Eve's children and God is a sinner for by law not was but IS accurate knowledge of sin says Paul...

Rom 3:20 Therefore by works of law no flesh will be declared righteous before him, for by law is the accurate knowledge of sin. (NWT, KIT)

So whether that sin was committed prior to the law or after the law, it is as sin to God, who does not change his concept of righteousness. People say that perfect genes remove the penalty for incest and so that was OK back then. But genetic imperfection is not why incest was prohibited. Incest defiles a family. It is an abuse of family love, and family love is the basis of all morality (which is merely a generalisation of that love). So God cannot have founded the house of Adam on incest. So Mark1 humans, pre-adamics, must have been converted to Mark2 and provided spouses for the children of Adam. Just as proseyltes could become Jews and just as Jews could become Christians. But then Eve (life) would not have been the mother of everyone living. Unless Eve had the conversion covenant. Eve must have been the door into Mark2 human flesh, adamic or non adamic, in order to preserve her position as the mother of all such flesh. She must have had the covenant for that fleshly conversion having been the first human to experience it through Adam's rib.

So Eve was the Mark1 to Mark2 conversion covenant mother to all the preadamics who become adamics and non adamics. And the women from that group were providing genetic children of Eve's behalf. So every human is a child either of Eve herself or of a pre adamic woman who was Mark2 coverted by Eve. And is therefore a covenant daughter of Eve. 

There are many mediators of salvation covenants, all men. Men are the priests of salvation, they give birth spiritually. Women are the priestesses of physical life. They give birth physically. Eve is the high priestess of physical life, of Mark2 adamic ageing fleshly bodies of what we call adamic flesh. And of Mark2 non adamic fleshly bodies. All physical human life is through her. But she is only one half of the equation.One is born again a second time. One enters into the womb of one's mother a 2nd time and is born again in the flesh OR one is born again angelically (or both). There are many many male mediators of salvation covenants. There is only one female mediator of Mark2 flesh (whether fallen or whether restored) and that is Eve and there is only one female mediator of angelic bodies and that is the Holy Spirit, the heavenly woman, Jerusalem above (Galatians 4:26 - heavenly Eve!

Earth:  Men: many mediators of salvation covenants — spiritual begetting (Abraham, Isaac, Jacob Moses). 
 Woman: one mediator of Mark2 flesh — Eve. High priestess of ageing, Adamic or non-Adamic bodies that still count as the second humanity. All such life is “through her” (womb or covenant-door).

Heaven: The matching priestess of the angelic body is the one woman above: Spirit / Jerusalem above / heavenly Eve. Paul already describes her as “Jerusalem above, mother of us” (Gal 4:26). He is naming her Eve’s counterpart.

Born again: John 3: Nicodemus hears “womb a second time” and Jesus points past that to water and Spirit. Nonetheless Nicodemuses words are scripture. So he provides a real track (flesh restored / Mark2 non adamic) and the angelic track. That is both/and by the maximal rule. The loaf of John 3 still privileges Spirit-birth; the second womb is the sense we refuse to kill because God put that apparent misunderstanding in the mouth of a teacher of Israel.

Half the equation is Eve (and her heavenly twin). The other half is the male line of covenant-fathers. One priestess of Mark2 flesh; many priests of rescue; one heavenly mother of angelic bodies.

3:20 then reads: she is mother of every living [Mark2 body]. Salvation-fathers are another office. Do not make Adam the only father and do not make every woman a second Eve. One Eve below, one Eve above.