פּירוש אויף בראשית 3:20

ויקרא האדם AND THE MAN CALLED — Scripture now reverts to its previous topic (Genesis 2:20) beginning with “and the man gave names”. It broke it off (that is, interpolated the story of the serpent) only to tell you that through the giving of names Eve became his mate, as it is written (Genesis 2:20) “but for Adam there was not found a help meet for him,” and that therefore “the [Lord God] caused to fall a deep sleep upon him” and formed Eve. But because Scripture writes at the end of the story of creation of Eve (Genesis 2:25), “and they were both naked”, it therefore follows on with the passage dealing with the serpent, to inform you that because he saw her nakedness and that they displayed no feeling of shame in their actions, he desired her, and he came upon them with his evil plan and with deceit.

Because she was the mother of all the living: And even though she was not the mother of the animals and the beasts, "mother" implies an expression of [being] a matron, as in (Judges 5:7), "I arose, a mother in Israel." And "father" is likewise an expression of lordship and authority, as in (Genesis 4:21), "the father of all who handle the lyre."

חוה, a variant of the word חיות, “life.” It is a derivative of the root: .הוה היה