The first question to be determined, of course, is: Did Peter have a throne? If he really was the early church's proto-pope, then it's reasonable to assume he had a throne—or at least something like it. And if he left a successor, who in turn left a successor and so on, then I suppose it's reasonable to say Francis is now the throne's rightful owner. This is the first question to consider since the mere fact of the office's existence deserves to be examined in light of the Word of God. After all, Catholics and Protestants take Scripture to be authoritative and infallible. A concept with such incredible import, then, must have some kind of biblical foundation. But does it?
To be fair, it's true the Lord Jesus distinguished Peter from the other disciples on several occasions. He was among the first to be called (Matt. 4:18) and his name always appears first on lists of the Twelve (Matt. 10:2, Mark 3:16). Jesus includes him among his closest disciples (Matt. 17:1). It was to Peter that Jesus said, "Feed my sheep" (John 21:17), and it was to Peter that he spoke the famous words: "You are Peter, and on this rock I will build my church, and the gates of hell shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven" (Matt 16:18-19).
However, it's not apparent in Scripture or church history that Peter had preeminence over his colleagues or other Christians. It's also not apparent that his fellow apostles, other local churches, or even Peter himself recognized his role in the church as exclusive in its representation of Jesus Christ. Certainly he was respected and revered as a leader, but these readily admitted realities do nothing to bolster Rome's contention that the pope functions as an infallible mouthpiece of God.
The Bible is clear on this point. The apostle Paul felt perfectly comfortable confronting and scolding Peter publicly when he acted improperly toward Gentile believers in Antioch (Gal. 2:11-14). Moreover, it was the apostle James—not Peter—who served as the leader at the Jerusalem Council (Acts 15) and when a decision was made it was sent on behalf of the "apostles and elders." Clearly, first-century Christians didn't esteem Peter in a separate category.
Matthew's Gospel corroborates this point, such that Jesus' promises to Peter were never understood as an exclusive delegation to Peter alone. In fact, just a few chapters later Matthew applies the same responsibility to the entire congregation:
If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector. Truly, I say to you, whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven. Again I say to you, if two of you agree on earth about anything they ask, it will be done for them by my Father in heaven. For where two or three are gathered in my name, there am I among them. (Matt. 18:15-18)
It's instructive to note how Paul viewed Peter. Along with Apollos and himself, Paul views Peter as a mere instrument through which God accomplishes his work (1 Cor. 3:22). He certainly recognizes Peter as a leader in the Jerusalem church—but among other apostles (Gal. 1:18-19). He mentions they were pillars of the church, but then proceeds to narrate the episode in which he openly confronted Peter (Gal. 2:11). Quite revealing is what Paul writes about his own calling: "For he who worked through Peter for his apostolic ministry to the circumcised worked also through me for mine to the Gentiles" (Gal. 2:8). According to Paul, then, the same Spirit enables these two apostles; no apostolic hierarchy exists.
Indeed, not even Peter saw himself as a primus inter pares. When he entered Cornelius's house to preach the gospel, the Roman centurion knelt before him in devotion. Peter, however, eschews the response: "Arise, I also am a man" (Acts 10:26). It seems no one in the first century—not even Peter himself—assumed Jesus intended him to be the unique intermediary on which the Christian church through all time would be built.
How Did God Preserve the Gospel?
This introduces a second question: Is there such a thing as legitimate Petrine succession? Here, it's apt to quote Peter's own words. In 2 Peter 1, aware of his impending death, he exhorts Christians to guard the memory of the gospel that the apostles had preached to them. And how does he do this? Not by pointing to a supreme successor, but by recording truth in the sacred pages of Scripture.
And we have the prophetic word more fully confirmed, to which you will do well to pay attention as to a lamp shining in a dark place, until the day dawns and the morning star rises in your hearts, knowing this first of all, that no prophecy of Scripture comes from someone's own interpretation. For no prophecy was ever produced by the will of man, but men spoke from God as they were carried along by the Holy Spirit. (2 Pet. 1:19-21)
So how did God design the preservation of his gospel? The answer isn't through a pope or person, but through a book written over centuries by persons "carried along by the Holy Spirit." God's trustworthy revelation in the gospel is preserved via the infallible, authoritative Word. It's clear Peter desires to leave a legacy, which these letters are sufficient to do as they keep Christians aware of all God desired them—and us—to know. There's no notion here of an eventual replacement, of someone taking his place to pass on to other successors the treasure of the Christian faith.
Put simply, I don't question Francis as the leader of the Roman Catholic Church. Nor do I question him as the legitimate papal successor to Benedict XVI. What I do question is any understanding of Christianity that puts forward Francis, Peter, or any other man as the exclusive, infallible head of the church—Christ's vicar with unique status before God.