The real reason that the Church proposes Mary to us as Christmas nears is because she is the model of how we should be living our advent.
Mary is, in some sense, Advent personified.
God the Father had prepared her from the first moment of her life to be a worthy mother of his Son. Like a faithful daughter of Israel, she had prayed throughout her youth for the coming of the Messiah. When she was a young girl, she discovered that she was part of God's answer to that prayer, but in a way that would far have exceeded any Hebrew maiden's prayers: not only would the Messiah be her son, but her son would also be God. Her "yes!" to the Archangel Gabriel launched the proximate preparation for the birth of Jesus the Messiah.
Each year we explicitly follow the footsteps Mary traced on that first Advent. We're entering into Mary's response of faith that are a guide for us along our own pilgrimage of faith. And so with the Lord, let us climb within Mary's womb and listen to the beat of her contemplative heart that was treasuring within this greatest of all mysteries, so that our Christmas may be as fruitful as that first Christmas.