The Catholic Church is apostolic because it is able to trace its lineage in unbroken continuity back to the Apostles.
Jesus said to Peter, “And I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it” (Matthew 16:18).
Speaking to all the Apostles, He said, “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you; and lo, I am with you always, to the close of the age” (Matthew 28:18-20).
Among the Apostles, Christ chose St. Paul to spread His Church. Speaking of him, Jesus said, “He is a chosen instrument of mine to carry my name before the Gentiles and kings and the sons of Israel; for I will show him how much he must suffer for the sake of my name” (Acts 9:15-16). Paul became the greatest missionary of all time. He brought the Gospel of Christ to the pagan world at the cost of great sacrifices.
To the Ephesians Paul wrote: “So then you are no longer strangers and sojourners, but you are fellow citizens with the saints and members of the household of God, built upon the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone” (Ephesians 2:19-20).
Since the days of the Apostles, episcopal power, that power held by the bishops, has been passed on through the Sacrament of Holy Orders, from generation to generation, from bishop to bishop. By the popes, bishops, priests, and deacons, the Gospel of Christ is preached in every part of the world, in fulfillment of the promise of Christ, “And I, when I am lifted up from the earth, will draw all men to myself” (John 12:32).