Why Precisely Do Catholics Refer Mary as “the Mother of God?

Question:
Why exactly do Catholics call Mary “the Mother of God”? How could God have a mother?
Answer
It’s not just Catholics who identify Mary as the Mother of God. Eastern Orthodox Christians also honour Mary as the theotokos, the God-bearer or birth-giver of God. Even Luther and Calvin accepted that Mary was the Mother of God (though Calvin did not wish people to use the title).
The prophecy of Isaiah 7:14 is applied to Jesus and Mary in Matthew 1:23. Mary is the virgin who gives birth to Emmanuel (God is with us). Probably the strongest Scriptural support for Mary as the Mother of God is in Luke 1:43, where Elizabeth speaks of Mary as “mother of my Lord.” The Greek word for Lord used here, “kyrios,” was used as a translation of the Hebrew word for God’s personal name, YHWH, spoken by Jews as “Adonai” or “Lord.” (Catechism of the Catholic Church, No. 446).Why, exactly, is Mary called “the Mother of God”? It is because she is the mother of the Word Incarnate who is divine. Numerous Scriptures identify Mary as the mother of Jesus (Jn 2:1; Mt 1:18, 2:11, 12:46). Since Jesus is God (cf. Jn 1:1), Mary must be seen as the one who bore God in her womb. Mary, of course, is not the mother of the Trinity or the divine nature of Jesus. Regardless, the person of the Word of God was the child she conceived in her womb and the child to whom she gave birth.
The belief in Mary as the Mother of God is a solemn dogma of the Catholic Church declared at the Council of Ephesus in 431.