Many non-Catholics may agree that Peter had a primacy in the early Church, even acting as the leading figure once Jesus ascended into Heaven. But they will say that this leadership of Peter was inherent to the apostolic age; there was no role per se of Peter that passed on after him.
These non-Catholics often say that there is no indication from the Bible that the leadership of Peter was meant to endure through his successors.
Historical evidence aside, doesn’t the very notion of “Keys of the Kingdom,” which were given to Peter (Matt 16:18-19), imply succession?
This is the solid evidence of Christ’s installation of Peter and successors.
Yes, the Keys do, and there is much more.
**Jesus explicitly made four promises to Peter alone: **
“You are Peter and on this rock I will build My Church.” (Mt 16:18)
“The gates of hell will not prevail against it.”(Mt 16:18)
“I will give you the keys of the Kingdom of heaven." (Mt 16:19)
“Whatever you bind on earth will be bound in heaven.” (Mt 16:19) [Later to the Twelve, also].
**Sole authority: **
“Strengthen your brethren.” (Lk 22:32)
“Feed My sheep.”(Jn 21:17).
Thus we see that Jesus very specifically formed His Church, and no other, on Peter the leader of the twelve Apostles. Further, the Sacred Scriptures emphasise:
The Church is “the pillar and bulwark of the truth (1 Tim 3:16).” St. Paul says also, “through the Church the manifold wisdom of God might now be made known to the principalities and powers in the heavenly places (Eph 3:10).” The Church teaches even the angels! This is with the authority of Christ!
“Beloved, do not trust every spirit but test the spirits to see whether they belong to God, because many false prophets have gone out into the world.” (1 Jn 4:1). St John counsels: “We belong to God, and anyone who knows God listens to us, while anyone who does not belong to God refuses to hear us. This is how we know the spirit of truth and the spirit of deceit.” (1 Jn 4:6 ).
Jesus, having given His authority to St Peter, confirmed: “I will not leave you orphans; I will come to you." (John 14:15-18) “The Advocate, the Holy Spirit that the Father will send in My name, He will teach you everything and remind you of all that I told you.” (John 14:26) “But when He comes, the Spirit of truth, He will guide you to all truth. He will not speak on His own, but He will speak what He hears, and will declare to you the things that are coming. He will glorify Me, because He will take from what is mine and declare it to you. Everything that the Father has is mine; for this reason I told you that He will take from what is mine and declare it to you.” (John 16:13-15).
Jesus warned dissenters: “if he refuses to hear even the Church let him be like the heathen and a publican.” (Mt 18:17).
Why on earth should a silly notion be accepted that Jesus did not intend His Truths in His Church to be present for mankind for all time?
The clincher is the Greet Commission to His Apostles:
"All power in heaven and on earth has been given to Me. Go, therefore, and make disciples of all nations, baptising 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, behold, I am with you always, until the end of the age.” (Mt 28: 18-20).
How foolish to concoct the idea that Christ would leave His Church with no one to lead Her on Peter’s death – no legitimate successor.