The fact remains that Paul said no such thing, calling Mary the new Eve.
Yet even though it is plain that Paul himself said no such thing, you contend that one can claim that Bergoglio can claim Paul said so, in the same way Matthew cites prophets in Matthew 2:23, persisting it be but by extrapolation?
Go ahead, establish the process of how Matthew extrapolated to reach the prophets having spoken of a one whom would be called a Nazarene apply to the Messiah, then let us see if that can be compared to how the Pope just said that Paul (not some unnamed prophets, but the Apostle Paul himself) said that Mary was the new Eve.
You did say the processes were the same.
Let us examine the processes to see if they are actually comparable (as you say they are).
As Jerome explained, Matthew did not in all instances alluded to of "as prophets spoke" (multiple prophets) need fully to "extrapolate" but in at least one instance (one of several prophet "speakers") used root forms (no pun intended?) of the meanings of the words as were written with it becoming straight away clearer in the Hebrew text.
The onus is upon yourself to prove that no one has been putting particular words into Paul's mouth (as seen in his writings) as Bergoglio obviously did when he said Paul spoke of Mary as "new Eve", for one simply cannot "extrapolate" from Paul, when he wrote of Jesus as the last Adam, that Paul was writing there also of Mary as "new Eve" without fully engaging in imposition upon both Pauline text themselves and the theology espoused therein.
Not also that Paul nowhere in Romans 5:12-20 & 1 Corinthians 5:45-49 uses the precise term "new" when speaking of Christ compared to Adam (you are a stickler for particular words are you not?) but instead speaks of Jesus as the last Adam (1 Co. 15:45) and when referring to his own comparison, refers to the Christ as the second man [in the comparison of two men, Adam & Jesus].
In 1 Co. 5 Paul writes of the first Adam being made of the dust. As sons of Adam in a sense, we are all of us "made of the dust" including Mary.
It was not Mary who came down from the heaven, but was instead the son which she bore in her own flesh, which flesh was "of the dust".
46 However, the spiritual is not first, but the natural; then the spiritual. 47 The first man is from the earth, [a]earthy; the second man is from heaven. 48 As is the earthy, so also are those who are earthy; and as is the heavenly, so also are those who are heavenly. 49 Just as we have borne the image of the earthy, [b]we will also bear the image of the heavenly.
Ourselves as bearing the image of the heavenly is by adoption by the Father, not adoption by the earthly mother Mary whom herself has no "heavenly mother" but is one of those (we would all like to freely assume) whom is also herself adopted by the Heavenly Father, even as she herself did bear the Christ as child, giving natural physical birth to the hypostasis which was the Messiah, him being both fully man and fully God -- after the tradition of the Hebrews the son being equal to the father.
"New" you say, as in "new Adam" ? Ok, the word "new" is workable when applied to Jesus as new Adam, causing no real injury, although it is slightly different from what Paul's own choice of words.
Yet you've been hanging your hat on "being right" when using that precise word, all while also demanding of others they show you yet another precise word, declaring victory for yourself in being "right" when all along you were a bit wrong in using the word "new" --- if we would be applying the same rigidity of standard equitably across the board.
In light of the texts which I have linked to written by Paul, there is no room for Ireneus in his own otherwise honest and correct efforts in asserting that Christ was indeed born a man by the virgin Mary, to then go further and to assign blame for sin entering the world upon Eve, which Ireneus does in the very same paragraph in which is found that which you brought of Ireneus, wherein at the end of that paragraph he speaks of Mary loosening the knot of Eve's disobedience.
Included in the reasoning employed to reach that conclusion, Ireneus wrote ;
"...But Eve was disobedient; for she did not obey when as yet she was a virgin. And even as she, having indeed a husband, Adam, but being nevertheless as yet a virgin (for in Paradise “they were both naked, and were not ashamed,” inasmuch as they, having been created a short time previously, had no understanding of the procreation of children: for it was necessary that they should first come to adult age, and then multiply from that time onward), having become disobedient, was made the cause of death, both to herself and to the entire human race; so also did Mary, having a man betrothed [to her], and being nevertheless a virgin, by yielding obedience, become the cause of salvation both to herself and the whole human race..."
Do I really now need to go to Paul, and from Romans 5 repeat Paul writing of how it was by one man that sin entered the world, and by one righteous act (Romans 5:18) one man's obedience (verse 19) resulted in the justification by which we are made righteous?
If there is any way to derive from the Apostle Paul him discussing a "new Eve", or even making room for such concept to then lead to justification [wink] for Ireneus to have written that Mary as "new Eve" became CAUSE OF SALVATION?
If so, then show how that occurs, and I'll show you an invention of Ireneus.
Yet another long winded post that changes nothing - and as usual you show up after everything is long settled.