Objection 1. It would seem that the Annunciation should not have been made by an angel to our Blessed Lady. For revelations to the highest angels are made immediately by God, as Dionysius says (Coel. Hier. vii). But the Mother of God is exalted above all the angels. Therefore it seems that the mystery of Incarnation should have been announced to her by God immediately, and not by an angel.
Objection 2. Further, if in this matter it behooved the common order to be observed, by which Divine things are announced to men by angels; in like manner Divine things are announced to a woman by a man: wherefore the Apostle says (1 Corinthians 14:34-35): "Let women keep silence in the churches... but if they would learn anything, let them ask their husbands at home." Therefore it seems that the mystery of Incarnation should have been announced to the Blessed Virgin by some man: especially seeing that Joseph, her husband, was instructed thereupon by an angel, as is related (Matthew 1:20-21)
Objection 3. Further, none can becomingly announce what he knows not. But the highest angels did not fully know the mystery of Incarnation: wherefore Dionysius says (Coel. Hier. vii) that the question, "Who is this that cometh from Edom?" (Isaiah 63:1) is to be understood as made by them. Therefore it seems that the announcement of Incarnation could not be made becomingly by any angel.
Objection 4. Further, greater things should be announced by messengers of greater dignity. But the mystery of Incarnation is the greatest of all things announced by angels to men. It seems, therefore, if it behooved to be announced by an angel at all, that this should have been done by an angel of the highest order. But Gabriel is not of the highest order, but of the order of archangels, which is the last but one: wherefore the Church sings: "We know that the archangel Gabriel brought thee a message from God" [Feast of Purification, B.V.M. ix Resp. Brev. O.P.]. Therefore this announcement was not becomingly made by the archangel Gabriel.
On the contrary, It is written (Luke 1:26): "The angel Gabriel was sent by God," etc.
I answer that, It was fitting for the mystery of Incarnation to be announced to the Mother of God by an angel, for three reasons. First, that in this also might be maintained the order established by God, by which Divine things are brought to men by means of the angels. Wherefore Dionysius says (Coel. Hier. iv) that "the angels were the first to be taught the Divine mystery of the loving kindness of Jesus: afterwards the grace of knowledge was imparted to us through them. Thus, then, the most god-like Gabriel made known to Zachary that a prophet son would be born to him; and, to Mary, how the Divine mystery of the ineffable conception of God would be realized in her."
Secondly, this was becoming to the restoration of human nature which was to be effected by Christ. Wherefore Bede says in a homily (in Annunt.): "It was an apt beginning of man's restoration that an angel should be sent by God to the Virgin who was to be hallowed by the Divine Birth: since the first cause of man's ruin was through the serpent being sent by the devil to cajole the woman by the spirit of pride."
Thirdly, because this was becoming to the virginity of the Mother of God. Wherefore Jerome says in a sermon on the Assumption [Ascribed to St. Jerome but not his work]: "It is well that an angel be sent to the Virgin; because virginity is ever akin to the angelic nature. Surely to live in the flesh and not according to the flesh is not an earthly but a heavenly life."
Reply to Objection 1. The Mother of God was above the angels as regards the dignity to which she was chosen by God. But as regards the present state of life, she was beneath the angels. For even Christ Himself, by reason of His passible life, "was made a little lower than the angels," according to Hebrews 2:9. But because Christ was both wayfarer and comprehensor, He did not need to be instructed by angels, as regards knowledge of Divine things. The Mother of God, however, was not yet in the state of comprehension: and therefore she had to be instructed by angels concerning the Divine Conception.
Reply to Objection 2. As Augustine says in a sermon on the Assumption (De Assump. B.V.M. [Work of another author: among the works of St. Augustine) a true estimation of the Blessed Virgin excludes her from certain general rules. For "neither did she 'multiply her conceptions' nor was she 'under man's, i.e. her husband's,' power (Genesis 3:16), who in her spotless womb conceived Christ of the Holy Ghost." Therefore it was fitting that she should be informed of the mystery of Incarnation by means not of a man, but of an angel. For this reason it was made known to her before Joseph: since the message was brought to her before she conceived, but to Joseph after she had conceived.
Reply to Objection 3. As may be gathered from the passage quoted from Dionysius, the angels were acquainted with the mystery of Incarnation: and yet they put this question, being desirous that Christ should give them more perfect knowledge of the details of this mystery, which are incomprehensible to any created intellect. Thus Maximus [Maximus of Constantinople] says that "there can be no question that the angels knew that Incarnation was to take place. But it was not given to them to trace the manner of our Lord's conception, nor how it was that He remained whole in the Father, whole throughout the universe, and was whole in the narrow abode of the Virgin."
Reply to Objection 4. Some say that Gabriel was of the highest order; because Gregory says (Hom. de Centum Ovibus [34 in Evang.): "It was right that one of the highest angels should come, since his message was most sublime." But this does nat imply that he was of the highest order of all, but in regard to the angels: since he was an archangel. Thus the Church calls him an archangel, and Gregory himself in a homily (De Centum Ovibus 34) says that "those are called archangels who announce sublime things." It is therefore sufficiently credible that he was the highest of the archangels. And, as Gregory says (De Centum Ovibus 34), this name agrees with his office: for "Gabriel means 'Power of God.' This message therefore was fittingly brought by the 'Power of God,' because the Lord of hosts and mighty in battle was coming to overcome the powers of the air."
Source: Summa Theologica (New Advent)