- The Hypostatic Union: Jesus Christ is fully God AND fully Man. God gave Mary the power, through the Holy Ghost, to produce a human body for the second person of the Holy Trinity. Jesus has two natures in one person.
To understand the title, "Mother of God," we must first clearly understand Mary's role as mother of our Savior, Jesus Christ. As Catholics, we firmly believe in the incarnation of our Lord: Mary conceived by the power of the Holy Spirit. (Cf. Lk 1: 26-38 and Mt 1: 18-25.) Through her, Jesus Christ second person of the Holy Trinity, one-in-being (consubstantial) with the Father, and true God from true God entered this world taking on human flesh and a human soul. Jesus is true God and true man. In His person are united both a divine nature and a human nature. Mary did not create the divine person of Jesus, who existed with the Father from all eternity: "In fact, the One whom she conceived as man by the Holy Spirit, who truly became her Son according to the flesh, was none other than the Father's eternal Son, the second person of the Holy Trinity. Hence the Church confesses that Mary is truly 'Mother of God' (Theotokos)" (Catechism, No. 495). As St. John wrote, "The Word became flesh and made His dwelling among us, and we have seen His glory: The glory of an only Son coming from the Father filled with enduring love" (Jn 1: 14).
For this reason, sometime in the early history of the Church, our Blessed Mother was given the title "Mother of God." St. John Chrysostom (d. 407), for example, composed in his Eucharistic Prayer for the Mass an anthem in honor of her: "It is truly just to proclaim you blessed, O Mother of God, who are most blessed, all pure and Mother of our God. We magnify you who are more honorable than the Cherubim and incomparably more glorious than the Seraphim. You who, without losing your virginity, gave birth to the Word of God. You who are truly the Mother of God. "
However, objection to the title "Mother of God" arose in the fifth century due to confusion concerning the mystery of the incarnation. Nestorius, Bishop of Constantinople (428-431), incited a major controversy. He stated that Mary gave birth to Jesus Christ, a regular human person, period. To this human person was united the person of the Word of God (the divine Jesus). This union of two persons the human Christ and the divine Word was "sublime and unique" but merely accidental. The divine person dwelt in the human person "as in a temple. " Following his own reasoning, Nestorious asserted that the human Jesus died on the cross, not the divine Jesus. As such, Mary is not "Mother of God," but simply "Mother of Christ" the human Jesus. Sound confusing? It is, but the result is the splitting of Christ into two persons and the denial of the incarnation.
From https://www.catholiceducation.org/en/culture/catholic-contributions/mary-the-mother-of-god.html
We must learn to give The Blessed Virgin Mary the honour and praise that is due to her. We can even "worship" her in a way, always knowing that, compared to God, she is less than an atom. (That is how St. Louis de Montfort expresses the relationship in the first chapter of his classic True Devotion to Mary)
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Divine Praises
Blessed be his holy Name.
Blessed be Jesus Christ, true God and true Man.
Blessed be the name of Jesus.
Blessed be his most Sacred Heart.
Blessed be his most Precious Blood.
Blessed be Jesus in the most holy Sacrament of the altar.
Blessed be the Holy Spirit, the Paraclete.
Blessed be the great Mother of God, Mary most holy.
Blessed be her holy and Immaculate Conception.
Blessed be her glorious Assumption.
Blessed be the name of Mary, Virgin and Mother.
Blessed be Saint Joseph, her most chaste spouse.
Blessed be God in his angels and in his saints.