"Eve, the wife of Adam, became the "mother of all the living," as we read in Genesis, chapter 3, verse 20. Because of Adam and Eve's disobedience to God, sin and death entered the world, and all of Eve's children are born in original sin. Through the obedience of Mary, the handmaid of the Lord, Jesus Christ entered the world as man to reverse the disobedience of Adam and Eve. For this reason, Christ is considered the "New Adam." Christ, the Son of Mary, offers a new life of grace to all who believe in Him. All who accept Christ's invitation become His brothers and sisters, and become the spiritual children of Mary, the New Eve."
The Scripture places the blame for sin entering into this world on Adam rather than Eve (Romans 5:12-21), with the reason being that the man received firsthand knowledge from God and yet still disobeyed. Paul develops a typological parallel between Christ and Adam: the former brought life upon mankind whereas the latter brought about death (1 Corinthians 15:45-47). Therefore, any notion of Mary being the new Eve collapses because the responsibility for the fall is attributed exclusively to Adam (even though the woman had sinned). Paul does not extend this parallel to Eve.
Early Christian writers such as Justin Martyr made parallels between Eve and Mary. Irenaeus wrote the following in his Against Heresies:
"For just as the former was led astray by the word of an angel, so that she fled from God when she had transgressed His word; so did the latter, by an angelic communication, receive the glad tidings that she should sustain (portaret) God, being obedient to His word. And if the former did disobey God, yet the latter was persuaded to be obedient to God, in order that the Virgin Mary might become the patroness (advocata) of the virgin Eve. And thus, as the human race fell into bondage to death by means of a virgin, so is it rescued by a virgin; virginal disobedience having been balanced in the opposite scale by virginal obedience. For in the same way the sin of the first created man (protoplasti) receives amendment by the correction of the First-begotten, and the coming of the serpent is conquered by the harmlessness of the dove, those bonds being unloosed by which we had been fast bound to death."
The articulated parallel does not amount to all of the theological developments within the Roman Catholic Church. It is not about Mary being a mediator of grace or an intercessor of sorts. Simply put, parallels are established between the fall and redemption with Jesus Christ being the central figure of preeminence as the new Adam. Irenaeus goes on to say:
"Christ gathered all things into one, by gathering them into himself. He declared war against our enemy, crushed him who at the beginning had taken us captive in Adam, and trampled on his head, in accordance with God’s words to the serpent in Genesis: I will put enmity between you and the woman, and between your seed and her seed; he shall lie in wait for your head, and you shall lie in wait for his heel [Genesis 3:15].”
Mary is like Eve in that she is a woman and that she gives birth to the promised seed. However, any idea of there being a salvific parallel between Mary and Eve goes beyond what is taught in Scripture. The authors of the New Testament nowhere apply a concept of divine motherhood to Mary over the church. Mary is blessed in that she found favor with God. But she is not greater in holiness and grace than any other believer in Jesus Christ. Mary is not the mother of a new humanity any more than was her own mother.
Furthermore, calling Mary the new Eve carries shocking implications that Roman Catholics themselves would obviously reject. Eve was married, gave birth to children, and was sinful. If there exists a connection, then that which is true of Eve must also be true of Mary. She also must have had children and a sinful nature. But all of that expressly conflicts with Roman Catholic theology. If Jesus is the last Adam and Mary is the new Eve, then it would seem to follow that an incestuous marriage was formed and that spiritual adultery also took place because the Scripture uses the analogy of a bride to describe the relationship between Christ and His church (which is all utterly blasphemous).