Mary is Mother of God because Jesus is God. This title was given to Mary at the Council of Ephesus in 431 in defense of Christ’s divinity. The Greek form of this title is Θεοτόκος (Theotokos) translated more literally as “God Bearer.”
Evidence for the celebration of this feast goes back in the Roman Church all the way to the 7th Century. Prior to that there is evidence of this feast being celebrated in other parts of Europe but usually on the Fourth Sunday of Advent. By the 13th and 14th Centuries However the Feast of the Circumcision of the Lord came to replace this feast, and the Feast of Mary Mother of God was eventually moved to October 11th and renamed the feast of the “Maternity of the Blessed Virgin Mary.” Just after Vatican II The more ancient Feast of Mary Mother of God was restored to January 1st.
That said, and as much as I love the Blessed Mother and affirm her under this proper title, I regret the loss of the Feast of the Circumcision. I generally prefer to stick as close to the Biblical narrative as possible. In this case Scripture is clear, on the eighth day (i.e. January 1st for us), Jesus was Circumcised and his name given. Three important truths and events are celebrated here. First that Jesus was born under the law and submitted himself to it so that he might fulfill it. Secondly there is the first shedding of blood, and this refers to the passion. Thirdly his name is announced: Jesus, a name which means “God saves.” There is no other name given to men by which we are to be saved, there is no other blood that can atone for our sins than the blood of Jesus and there is no one who can fulfill the Law as Jesus does. It seems a bit of a loss not to explicitly celebrate these events in Jesus life and these truth about him on the very day (the eighth day) they happened.
Our thoughts now turn spontaneously to Our Lady, whom we invoke today as the Mother of God. It was Pope Paul VI who moved to 1 January the Feast of the Divine Motherhood of Mary, which was formerly celebrated on 11 October. Indeed, even before the liturgical reform that followed the Second Vatican Council, the memorial of the circumcision of Jesus on the eighth day after his birth – as a sign of submission to the law, his official insertion in the Chosen People – used to be celebrated on the first day of the year and the Feast of the Name of Jesus was celebrated the following Sunday. We perceive a few traces of these celebrations in the Gospel passage that has just been proclaimed, in which St Luke says that eight days after his birth the Child was circumcised and was given the name “Jesus”, “the name given by the Angel before he was conceived in [his Mother’s]… womb” (Lk 2: 21). Today’s feast, therefore, as well as being a particularly significant Marian feast, also preserves a strongly Christological content because, we might say, before the Mother, it concerns the Son, Jesus, true God and true Man.