"That the Lord then was manifestly coming to His own things, and was sustaining them by means of that creation which is supported by Himself, and was making a recapitulation of that disobedience which had occurred in connection with a tree, through the obedience which was [exhibited by Himself when He hung] upon a tree, [the effects] also of that deception being done away with, by which that virgin Eve, who was already espoused to a man, was unhappily misled,—was happily announced, through means of the truth [spoken] by the angel to the Virgin Mary, who was [also espoused] to a man. 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."
- St. Irenaeus, Against Heresies, V:19:1, The Apostolic Fathers with Justin Martyr and Irenaeus by Philip Schaff, first published in Edinburgh, 1867, Christian Classics Ethereal Library.
Thus, Irenaeus, writing in the late second century, connects the simplicity of the dove with Mary, seen as the new Eve ("as the human race fell into bondage to death by means of a virgin, . . . 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.")
Looking at the various "dove" passages in Scripture, in and of themselves, it is difficult to know whether Jesus really had the Old Testament passages in mind when he said to be as wise as serpents and harmless as doves, so that it is not immediately possible to connect the "dove" symbolism in the Song of Songs -- in which St. Bernard of Clairvaux and St. John of the Cross would both see the dove as symbolic of the Church -- with the "dove" symbolism in the Gospel -- in which Jesus said to be as wise as serpents and harmless as doves. St. Irenaeus ties it a little more together with Mary, comparing Mary as the New Eve with the simplicity of the dove.
St. Edith Stein, in her Essays on Woman, has a great deal to say about Mary as the New Eve and Mary as the heart of the Church. Such an understanding of Mary helps to tie together the symbolic understanding of the dove in St. Irenaeus, St. John of the Cross, St. Bernard of Clairvaux, Bl. Hildegard of Bingen, and St. Augustine, discussed here, and there is much poetry and mysticism in their respective references to it. St. Edith Stein probably said nothing original or unique in the passages quoted here, but she said it well, when she wrote of Mary as the new Eve and as the symbol of the Church, the heart of the Church:
"The creation of Eve from the rib of the first Adam becomes a prefigurement for the emergence of the new Eve -- by that is meant Mary, but, at the same time, also the whole Church -- from the opened side of the new Adam. The woman who is bound to her husband in true Christian matrimony, that is, in an indissoluble union of life and love, represents the Church as God's bride. Even more impressively and perfectly, the Church is personally embodied in the woman who as Spouse of Christ has consecrated her life to the Lord and has entered into an indissoluble contract with Him. She herself stands at His side like the Church, and assists in His work of redemption like its prototype, the Mother of God, in whom it has its origin. The complete surrender of her life and being is to live and work with Christ; but that means also to suffer and die with Him -- that fruitful death from which springs the life of grace for all humanity. And so the life of God's bride becomes supernatural maternity for all of redeemed humanity, whether she works directly with the soul herself or whether she only brings forth through her sacrifice the fruits of grace, of which she and perhaps no other has knowledge.
"Mary is the most perfect symbol of the Church because she is its prefigurement and origin. She is also a unique organ of the Church, that organ from which the entire Mystical Body, even the Head itself, was formed. She might be called, and happily so, the heart of the Church in order to indicate her central and vital position in it. . . . The title of Mary as our mother is not merely symbolic. Mary is our mother in the most real and lofty sense, a sense which surpasses that of earthly maternity. She begot our life of grace for us because she offered up her entire being, body and soul, as the Mother of God."
- St. Edith Stein, "Church, Woman, Youth", Essays on Woman.