The Catholic Church was Founded by Christ

"And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it."

Matthew 16:18
Introduction

There are some who erroneously claim that the Catholic Church is a man-made organization with no connection to Christ. As Catholics, we believe the Catholic Church was founded by Christ and inseparable from His Body. The Church is manifest in three dimensions, which together make up the Mystical Body of Christ. The Church Triumphant of the redeemed in heaven; the Church Suffering of those being purified in Purgatory; and the earthly Church Militant of those struggling against the evils of this world. The Catholic Church is the Kingdom of God. The earthly kingdom of the Church Militant is ruled in His absence by men (Mt. 18:18; Jn. 21:17). It is therefore a visible theocracy; and it was substituted for the Jewish theocracy that has rejected Him (Mt. 21:43). In it, until the Day of Judgment, the bad will be mingled with the good (Mt. 13:41). Its extent will be universal (Mt. 28:19), and its duration to the end of time (Mt. 13:49); all powers that oppose it shall be crushed (Mt. 21:44). Moreover, it will be a supernatural kingdom of truth, in the world, though not of it (Jn. 18:36). It will be one and undivided, and this unity shall be a witness to all men that its founder came from God (Jn. 17:21).

Catechism
It was the Son's task to accomplish the Father's plan of salvation in the fullness of time. Its accomplishment was the reason for his being sent. "The Lord Jesus inaugurated his Church by preaching the Good News, that is, the coming of the Reign of God, promised over the ages in the scriptures." To fulfill the Father's will, Christ ushered in the Kingdom of heaven on earth. The Church "is the Reign of Christ already present in mystery."
- Catechism of the Catholic Church, 2nd ed., (1997), n.763
The Lord Jesus endowed his community with a structure that will remain until the Kingdom is fully achieved. Before all else there is the choice of the Twelve with Peter as their head. Representing the twelve tribes of Israel, they are the foundation stones of the new Jerusalem. The Twelve and the other disciples share in Christ's mission and his power, but also in his lot. By all his actions, Christ prepares and builds his Church.
- Catechism of the Catholic Church, 2nd ed., (1997), n.765
The Church is both the means and the goal of God's plan: prefigured in creation, prepared for in the Old Covenant, founded by the words and actions of Jesus Christ, fulfilled by his redeeming cross and his Resurrection, the Church has been manifested as the mystery of salvation by the outpouring of the Holy Spirit. She will be perfected in the glory of heaven as the assembly of all the redeemed of the earth.
- Catechism of the Catholic Church, 2nd ed., (1997), n.778
Scripture

2 Sam. 7:16; Ps. 88:4-5; 1 Chron. 17:12,14 - God promises to establish a Davidic kingdom forever on earth.

Ezek. 37:24-25 - David will be king over them forever with one shepherd. Jesus is King, and Peter is our earthly shepherd.

Mt. 16:18 - Jesus founded the Church on Peter. There’s only one Church built upon one Rock with one teaching authority.

Mt. 18:17-19 - Jesus exhorts people to seek the Church as a final authority and bestows upon it divine gifts.

Tradition & Fathers
"Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church."
- St. Ignatius of Antioch, Epistle to the Smyrnaens (A.D. ~30-108)
"[God hath set] all the other means through which the Spirit works; … For where the Church is, there is the Spirit of God; and where the Spirit of God is, there is the Church, and every kind of grace; but the Spirit is truth."