1. Office of Pope
The proof that Christ constituted St. Peter head of His Church is found in the two famous Petrine texts, Matthew 16:17-19, and John 21:15-17.
Matthew 16:17-19 In Matthew 16:17-19, the office is solemnly promised to the Apostle. In response to his profession of faith in the Divine Nature of his Master, Christ thus addresses 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 on earth it shall be bound also in heaven: and whatsoever thou shalt loose on earth, it shall be loosed also in heaven.
"Blessed art thou, Simon Bar-Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven." The prerogatives here promised are manifestly personal to Peter. His profession of faith was not made as has been sometimes asserted, in the name of the other Apostles. This is evident from the words of Christ. He pronounces on the Apostle, distinguishing him by his name Simon son of John, a peculiar and personal blessing, declaring that his knowledge regarding the Divine Sonship sprang from a special revelation granted to him by the Father (cf. Matthew 11:27).
"And I say to thee: That thou art Peter. . ." He further proceeds to recompense this confession of His Divinity by bestowing upon him a reward proper to himself:
Thou art Peter [Cepha, transliterated also Kipha] and upon this rock [Cepha] I will build my Church.
The word for Peter and for rock in the original Aramaic is one and the same; this renders it evident that the various attempts to explain the term "rock" as having reference not to Peter himself but to something else are misinterpretations. It is Peter who is the rock of the Church. The term ecclesia (ekklesia) here employed is the Greek rendering of the Hebrew qahal, the name which denoted the Hebrew nation viewed as God's Church.
"And upon this rock I will build my Church. . ." Here then Christ teaches plainly that in the future the Church will be the society of those who acknowledge Him, and that this Church will be built on Peter.
The expression presents no difficulty. In both the Old and New Testaments the Church is often spoken of under the metaphor of God's house (Numbers 12:7; Jeremiah 12:7; Hosea 8:1; 9:15; 1 Corinthians 3:9-17, Ephesians 2:20-2; 1 Timothy 3:5; Hebrews 3:5; 1 Peter 2:5). Peter is to be to the Church what the foundation is in regard to a house.
He is to be the principle of unity, of stability, and of increase. He is the principle of unity, since what is not joined to that foundation is no part of the Church; of stability, since it is the firmness of this foundation in virtue of which the Church remains unshaken by the storms which buffet her; of increase, since, if she grows, it is because new stones are laid on this foundation.
"And the gates of hell shall not prevail against it." It is through her union with Peter, Christ continues, that the Church will prove the victor in her long contest with the Evil One:
The gates of hell shall not prevail against it.