Why is the Catholic Church called the Mystical Body of Christ?

Baltimore Catechism:  Back to the Roots of Traditional Catholicism

The Catholic Church is called the Mystical Body of Christ Because its members are united by supernatural bonds with one another and with Christ, their Head, thus resembling the members and head of the living human body.
When the Father looks down from heaven at the Church, He sees Christ. THE CHURCH IS CHRIST. It is His body of which He is the Head and we are the members.

When Christ, our Head, looks down from the Cross at the Church, He sees Mary. THE CHURCH IS MARY. She is Holy Mother Church, containing, as it were, all the members of the Church in herself to unite them to Christ, our Head.

Mary is the Mother of Christ in the flesh, but in the life of grace, she is His bride. Her divine life came from His, not His from hers.
What Pope Pius XII says of the Church is true of her, "As a second Eve she came forth from the side of the new Adam in His sleep on the Cross." She is the new Eve leading all her children to the Cross, the tree of life, to drink from Christ's open side the living waters of the Holy Ghost, the new wine of holy love.

Our Lord showed St John the meaning of what had happened on Mt. Calvary, using Jerusalem as a symbol for Mary, Mother of the Church.

Come, I will show thee the bride, the spouse of the Lamb.' And he took me up in spirit to a mountain great and high and showed me the holy city Jerusalem, coming down out of heaven from God, having the glory of God...In the midst of the city street, on both sides of the river, was the tree of life: (Apoc. 21, 9-11;22,2).