She is the "Mother Of GOD", as shown in Holy Scripture, and
by reasoning. She is the Mother of Jesus Christ.
Matthew 16:18, "And I say to thee, thou art Peter, and Upon this rock I will build MY CHURCH, and the Gates of Hell shall not prevail against it."
Ephesians 1:22-23, "And all things He made subject under His feet, and Him He gave as head over all the Church, which indeed is His Body, the completion of Him who fills all with all."
Colossians 1:18, "Again, he is the head of the body, the Church..."
Romans 12:5, "...so we, the many, are one body in Christ, but severally members one of another."
Jesus Christ founded a Church of which He is the Head and His Body is all of us.
As a mother, she bore Jesus Christ, just as in Baptism we are born into the Church, John 3:3-7.
As a mother, she fed Him, just as in the Church we are spiritually fed by the Sacraments.
John 19:26, "When Jesus, therefore, saw His Mother and the disciple standing by, whom He loved, He said to His Mother, "Woman, behold, thy Son." Then He said to the disciple, "Behold, thy Mother". And from that hour the disciple took her into his home."
We all know the disciple Jesus referred to as, "whom He loved", was the Apostle John. Why didn't John use his name here when he wrote his Gospel instead of the wording that he did use? It is because "the disciple whom Jesus loved" is all of us. We are all His disciples, and He loves all of us. It becomes obvious if you reverse it and say, "Then He did not love His other disciples, only John, or was John the only disciple He loved?"
Since the Son IS the Church, along with the rest of us, then His Mother is rightfully,
the Mother of the Church.