Thanks for your reply. What follows is not specific to Catholicism but is common to most Protestant theologies as well.
That the Son was homoousios (of same substance) as the Father goes back to and before Nicene Creed which declared the full divinity and full humanity of Jesus. We do not hold that Mary is the mother of God the Father or the mother of the Holy Trinity, but mother of God the Son.
Orthodox (trinitarian) theology, that Jesus is fully human and fully God, (this is contra various heresies referred to earlier.
The Council of Chalcedon, which Anglicans and most Protestants hold as ecumenical, declared that in Christ there are two natures; each retaining its own properties, and together united in one subsistence and in one single person - a hypostatic union - which cannot be separated and still be Jesus.
If we hold that Mary gave birth to Jesus the human, but not Jesus God, we split what cannot be split - Jesus, fully human and fully divine. If we say Mary gave birth to one nature of Jesus and not the other nature, we err, because mothers give birth to persons not natures. Jesus is a person who was born of a woman, Mary.
Monophysites and Nestorians disagree on the person of Christ and therefore have a different Christology, heretical to Orthodox Trinitarian Christianity.
Okay, let me dip my toe into this as well.
Questions:
Did Jesus exist before Mary existed?
Since we agree that Jesus is both human and divine, when you say they cannot be separated, then did God the Son die on the cross? The human nature had a beginning, did it not?
You say mothers give birth to persons, yet do they not really give birth to a body that contains a personal spirit? Some mothers give birth to stillborn babies. They are persons, they have bodies, yet they do not have a spirit anymore.
Why did the Roman Catholic Church's magesterium go against the teachings of some of their revered "fathers" who disputed that Mary was the "Mother of God"? You DO know it was not universally accepted, don't you?
Finally, why didn't the "all-wise, Holy Spirit led" magesterium understand that they could have avoided the controversy by explaining the incarnation more clearly without assigning God-birthing to a human being? How many organizations exist today that are devoted to the Virgin Mary and who only acknowledge Jesus Christ in passing? Do you believe that is how it should be?