Why is the Catholic Church called the Mystical Body of Christ? 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.
Again, he is the head of his body, the Church. (Colossians 1:18)
What conditions are necessary in order that a person be a member of the Mystical Body in the full sense? In order that a person be a member of the Mystical Body in the full sense, it is necessary that he be baptized, that he profess the Catholic faith, and that he neither separate himself from the Mystical Body nor be excluded by lawful authority.
And if he refuses to hear them, appeal to the Church, but if he refuses to hear even the Church, let him be to thee as the heathen and the publican. (Matthew 18:17)
Further reading: CCC 787-789