Objection 1. It would seem that the Annunciation did not take place in becoming order. For the dignity of the Mother of God results from the child she conceived. But the cause should be made known before the effect. Therefore the angel should have announced to the Virgin the conception of her child before acknowledging her dignity in greeting her.
Objection 2. Further, proof should be omitted in things which admit of no doubt; and premised where doubt is possible. But the angel seems first to have announced what the virgin might doubt, and which, because of her doubt, would make her ask: "How shall this be done?" and afterwards to have given the proof, alleging both the instance of Elizabeth and the omnipotence of God. Therefore the Annunciation was made by the angel in unbecoming order.
Objection 3. Further, the greater cannot be adequately proved by the less. But it was a greater wonder for a virgin than for an old woman to be with child. Therefore the angel's proof was insufficient to demonstrate the conception of a virgin from that of an old woman.
On the contrary, it is written (Romans 13:1): "Those that are of God, are well ordered [Vulgate: 'Those that are, are ordained of God']." Now the angel was "sent by God" to announce unto the Virgin, as is related Luke 1:26. Therefore the Annunciation was made by the angel in the most perfect order.
I answer that, The Annunciation was made by the angel in a becoming manner. For the angel had a threefold purpose in regard to the Virgin. First, to draw her attention to the consideration of a matter of such moment. This he did by greeting her by a new and unwonted salutation. Wherefore Origen says, commenting on Luke (Hom. vi), that if "she had known that similar words had been addressed to anyone else, she, who had knowledge of the Law, would never have been astonished at the seeming strangeness of the salutation." In which salutation he began by asserting her worthiness of the conception, by saying, "Full of grace"; then he announced the conception in the words, "The Lord is with thee"; and then foretold the honor which would result to her therefrom, by saying, "Blessed art thou among women."
Secondly, he purposed to instruct her about the mystery of the Incarnation, which was to be fulfilled in her. This he did by foretelling the conception and birth, saying: "Behold, thou shalt conceive in thy womb," etc.; and by declaring the dignity of the child conceived, saying: "He shall be great"; and further, by making known the mode of conception, when he said: "The Holy Ghost shall come upon thee."
Thirdly, he purposed to lead her mind to consent. This he did by the instance of Elizabeth, and by the argument from Divine omnipotence.
Reply to Objection 1. To a humble mind nothing is more astonishing than to hear its own excellence. Now, wonder is most effective in drawing the mind's attention. Therefore the angel, desirous of drawing the Virgin's attention to the hearing of so great a mystery, began by praising her.
Reply to Objection 2. Ambrose says explicitly on Luke 1:34, that the Blessed Virgin did not doubt the angel's words. For he says: "Mary's answer is more temperate than the words of the priest. She says: How shall this be? He replies: Whereby shall I know this? He denies that he believes, since he denies that he knows this. She does not doubt fulfilment when she asks how it shall be done."
Augustine, however, seems to assert that she doubted. For he says (De Qq. Vet. et Nov. Test. qu. li): "To Mary, in doubt about the conception, the angel declares the possibility thereof." But such a doubt is one of wonder rather than of unbelief. And so the angel adduces a proof, not as a cure for unbelief, but in order to remove her astonishment.
Reply to Objection 3. As Ambrose says (Hexaemeron v): "For this reason had many barren women borne children, that the virginal birth might be credible."
The conception of the sterile Elizabeth is therefore adduced, not as a sufficient argument, but as a kind of figurative example.: consequently in support of this instance, the convincing argument is added taken from the Divine omnipotence.
Source: Summa Theologica (New Advent)