From a commentary by Ambrose of Milan on Saint Luke's Gospel
The angel Gabriel had announced the news of something that was as yet hidden and so, to buttress the Virgin Mary’s faith by means of a real example, he told her also that an old and sterile woman had conceived, showing that everything that God willed was possible to God.
When Mary heard this she did not disbelieve the prophecy, she was not uncertain of the message, she did not doubt the example: but happy because of the promise that had been given, eager to fulfil her duty as a cousin, hurried by her joy, she went up into the hill country.
Where could she hurry to except to the hills, filled with God as she was? The grace of the Holy Spirit does not admit of delays. And Mary’s arrival and the presence of her Son quickly show their effects: As soon as Elizabeth heard Mary’s greeting her child leapt in her womb and she was filled with the Holy Spirit.
See the careful distinction in the choice of words. Elizabeth was the first to hear the voice but her son John was the first to feel the effects of grace. She heard as one hears in the natural course of things; he leapt because of the mystery that was there. She sensed the coming of Mary, he the coming of the Lord; the woman knew the woman, the child knew the child. The women speak of grace while inside them grace works on their babies. And by a double miracle, the women prophesy under the inspiration of their unborn children.
The infant leapt and the mother was filled with the Spirit. The mother was not filled before her son: her son was filled with the Holy Spirit and in turn, filled his mother. John leapt and so did Mary’s spirit. John leapt and filled Elizabeth with the Spirit, but we know that Mary was not filled but her spirit rejoiced. For the Incomprehensible was working incomprehensibly within his mother. Elizabeth had been filled with the Spirit after she conceived, but Mary before, at the moment the angel had come. “Blessed are you,” said Elizabeth, “who believed”.
You too, my people, are blessed, you who have heard and who believe. Every soul that believes, that soul both conceives and gives birth to the Word of God and recognises his works.
Let the soul of Mary be in each one of you, to proclaim the greatness of the Lord. Let the spirit of Mary be in each one of you, to rejoice in God. According to the flesh, only one woman can be the mother of Christ but in the world of faith, Christ is the fruit of all of us. For every soul can receive the Word of God if only it is pure and preserves itself in chastity and modesty.
The soul that has been able to reach this state proclaims the greatness of the Lord just as Mary did and rejoices in God its saviour just like her.
The Lord’s greatness is proclaimed, as you have read elsewhere, where it says, "Join me in magnifying the Lord."
This does not mean that anything can be added to the Lord’s greatness by human words, but that he is magnified in us. Christ is the image of God and so any good or religious act that a soul performs magnifies that image of God in that soul, the God in whose likeness the soul itself was made. And thus the soul itself has some share in his greatness and is ennobled.