That is EXACTLY what Adam is saying here. Exactly.
Gen 3:20
And Adam called his wife's name Eve;
because she was the mother of all living.
Gen 3:15
And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.
Adam immediately called her "mother of all living" after hearing this prophecy. He SHOULD have called her the mother of all dead. But of course he does not. Adam KNEW that the "Son of promise" would come through HER.....without HIM!
Rom 5:12
Wherefore, as by one
man sin entered into the world, and death by sin; and so death passed upon
all men, for that all have sinned:
Sin entered the WORLD.....thru Adam's willful sin, as he is the federal head.
When Eve sinned.....sin entered......EVE. Nobody else!
Hope that clears up this much debated issue.