Matthias filled the OFFICE vacated by Judas, but there isn’t any reason to think that the office was that of a traitor…all we know is that Judas, personally, was a traitor and unworthy of the office.
The office of the Bishop of Rome is also one that extends after the death of Peter, and I would like to explain that as follows:
Peter – The Rock, Keeper of the Keys and Royal Steward
"When Jesus came to the region of Caesarea Philippi, he asked his disciples, “Who do people say the Son of Man is?” They replied, “Some say John the Baptist; others say Elijah; and still others, Jeremiah or one of the prophets.” “But what about you?” he asked. “Who do you say I am?” Simon Peter answered, “You are the Christ, the Son of the living God.” Jesus replied, “Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven. And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it. I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.” (Matthew 16:13-19)
Peter’s understanding that Jesus was the Son of God did not come from working it out on his own; God the Father infused this revelation into Peter’s mind thus imprinting His seal of approval upon the humble fisherman. In turn, Jesus recognized that Simon had already been anointed by His Father in this way, and He declared, “Blessed are you” because the Father had already blessed Simon with knowledge of the Son. Speaking in His native tongue, Aramaic, Jesus gave Simon a new name, “Kepha”, the Aramaic word that means “rock”. Jesus declared, “You are kepha, and on this kepha I will build my church.”
Although Jesus spoke Aramaic, the New Testament was written in Greek, and “Kepha” would have been translated into the Greek words for “rock” which are “petra” or “petros”. “Petra” is the feminine form of the masculine word, “petros”, and obviously, “petros” is the more suitable form for a man’s name. From “petros” we derive the English name, “Peter”. For us modern readers then, Jesus’ pronouncement reads, “You are Peter and upon this rock I will build my church”, but we must never lose sight of the fact that in the original language used by Jesus, Simon is clearly identified as the rock upon which the Church would be built by Jesus. Jesus announced His intention to establish His Church (singular – not “churches” plural) and His choice of Peter as its leader.
What is it about Peter’s character that caused Jesus to compare him to something as solid as rock? Isn’t this the same Peter who Jesus called “Satan” just a few verses later? (cf. Mt 16:23) Isn’t this the same Peter who would deny the Lord three times after his arrest? (cf. Lk 22:34) Surely this unstable character is anything but solid rock upon which a Church could be built; yet, Jesus sees something deeper in Peter’s character, and His choice would be vindicated when Peter ultimately received a martyr’s crown via crucifixion.
Matthew also tells us that Jesus gave Peter the “keys of the kingdom of heaven”. In ancient times, a king might choose a second in command (known as the royal steward) who literally wore a large key as a symbol of his office and who spoke with the authority of the king. The prophet Isaiah confirms this:
"In that day I will summon my servant, Eliakim son of Hilkiah. I will clothe him with your robe and fasten your sash around him and hand your authority over to him. He will be a father to those who live in Jerusalem and to the house of Judah. I will place on his shoulder the key to the house of David; what he opens no one can shut, and what he shuts no one can open.” (Isaiah 22:22)
In the passage above, God is speaking, and He confirms the existence of the office, the key, and the continuation of the office despite the change of office holder. In other words, the office of the royal steward continued even when the man who held the office died or was replaced by someone else.
How does this relate to what we have learned from Matthew? In the New Testament, we learn that Jesus inherits the throne of his father, David.
And behold, you will conceive in your womb and bear a son, and you shall call his name Jesus. He will be great, and will be called Son of the Most High; and the Lord God will give to him the throne of his father David, and he will reign over the house of Jacob forever; and of his kingdom there will be no end. (Luke 1:31–33)
Thus, we know that Jesus is a king who will reign forever. Matthew tells us that that King Jesus named Peter as His royal steward and gave him the “keys to the kingdom of heaven" as the symbol of his authority to speak in His name. Since Jesus is an eternal king, the office of royal steward in His kingdom will never end. Although Peter died as a martyr (as Jesus foretold), the successors of Peter have taken his place in the eternal office of royal steward that Jesus established in His royal court.
In addition to the reference to a key or keys, note the following parallels:
"What he opens no one can shut, and what he shuts no one can open.” (Is. 22:22)
"Whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.” (Mt. 16:19)
Jesus was thoroughly familiar with the Old Testament scriptures, and He intentionally referenced the passage from Isaiah when He appointed Peter as His royal steward.