Jesus Christ Himself, in the 16th chapter of St. Matthew:
"And Jesus came into the quarters of Cesarea Philippi: and he asked his disciples, saying: Whom do men say that the Son of man is? But they said: Some John the Baptist, and other some Elias, and others Jeremias, or one of the prophets. Jesus saith to them: But whom do you say that I am? Simon Peter answered and said: Thou art Christ, the Son of the living God. And Jesus answering said to him: Blessed art thou, Simon Bar-Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven. 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. And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shalt loose on earth, it shall be loosed also in heaven.." [St. Matt. 16:13-19]
"Going therefore, teach ye all nations: baptizing them in the name of the Father and of the Son and of the Holy Ghost. Teaching them to observe all things whatsoever I have commanded you. And behold I am with you all days, even to the consummation of the world." [St. Matt 28:19-20]
"He that heareth you heareth me: and he that despiseth you despiseth me: and he that despiseth me despiseth him that sent me." [St. Luke 10:16]
"But if I tarry long, that thou mayest know how thou oughtest to behave thyself in the house of God, which is the church of the living God, the pillar and ground of the truth." [1 Tim 3:15]
"If Christ did set up such an organization [the Church], he must have provided for its continuation, for its easy identification (that is, it had to be visible so it could be found), and, since he would be gone from earth, for some method by which it could preserve his teachings intact.And that same Church exists today: the Cathloic Church, connected to Ss. Peter and Paul (and thence to Our Lord) by direct apostolic succession.All this was accomplished through the apostolic succession of bishops, and the preservation of the Christian message, in its fullness, was guaranteed through the gift of infallibility, of the Church as a whole, but mainly through the its Christ-appointed leaders, the bishops (as a whole) and the pope (as an individual).
It is the Holy Spirit who prevents the pope from officially teaching error, and this charism follows necessarily from the existence of the Church itself. If, as Christ promised, the gates of hell will not prevail against the Church then it must be protected from fundamentally falling into error and thus away from Christ. It must prove itself to be a perfectly steady guide in matters pertaining to salvation." [Source]
Since today is the feast of St. Ignatius of Antioch, the person who coined the term "Catholic Church", I'll let him explain, in the words of his second-century letter [A.D. 110] to the church in Smyrna: "Wherever the bishop appears, let the people be there; just as wherever Jesus Christ is, there is the Catholic Church".
Yours in Christian fraternity,
B-chan