Catholic doctrine teaches that the Church is not merely an external organization, but a mystery: the communion of those gathered by the Holy Spirit, united with Christ as His Body, under the high priesthood of Jesus and serving the mission of proclaiming the Gospel. The accounts of Matthew and the letter to the Corinthians are mentioned only thematically; no lengthy quotations are given.
Jesus entrusted to Peter and the Apostles the foundation of unity and mission. The Catechism (Part One, Section Three on the Church) and the documents on vatican.va are standard references for teaching on catholicity, apostolicity, and communion.
Two foundations commonly encountered in parishes: Jesus gave Peter a key role in the plan to build the Church (Matthew 16 narrative; please read the entire passage from 13–20 for the context of the “rock” and the confession). The first letter to the Corinthians uses the image of one body, many members in Christ (chapter 12 — it is advisable to read the whole chapter, not just a few verses).
Compare with the original
Open Matthew 16:13–20 and 1 Corinthians 12 in an approved Bible; this article does not quote lengthy passages.
Communion
The Catholic Church emphasizes communion (koinonia): with the Triune God, with one another in the Sacraments, and with the Pope and bishops in communion as a sign of unity.
Lumen Gentium: People of God, Body of Christ, Temple of the Holy Spirit
The Constitution Lumen Gentium on the Church presents three intrinsically linked images: People of God gathered by God; Body of Christ of which Christ is the Head; Temple of the Holy Spirit sanctified from within. This expression does not allow the Church to be reduced to a merely secular “non-profit organization,” nor to be so mystified as to forget its visible structure and apostolic ministry. The Catechism Part One, Section Three on the Church, systematizes the attributes One, Holy, Catholic, Apostolic as the marks of the Church established by Christ. Thus, Matthew 16:18 and 1 Corinthians 12 are not mere slogans but an invitation to live responsibly in the Body: each member has a role, all serve the common mission under the one Head, Jesus.
