In simple English, the belief of papal succession includes with it the power of appointing all ‘true officers’ of the ‘true church’. In other words, in practice it is simply the Roman Catholic means of doctrinally excluding all other Christian churches. More to the point it makes any persons personal salvation outside her physical ordained network- 'doubtful to none'. 'Doubtful' if they are not properly introduced to Catholic authority, 'none' if they are and yet adamantly reject it, like most Protestant teachers and pastors.
Note: To post an answer that respects current Roman Catholic beliefs, I actually had to have something critical clarified in my own mind. I raised this post to really understand the ultimate impact of belief in papal succession: Do Catholics officially recognize Protestants as Christians?
I have not encountered ‘the’ biblical argument against papal succession but I have run across several versions. The points of argument that have made the biggest impact for me as a Protestant are:
There is no biblical argument for papal succession anywhere to be found in the Bible. Any attempts that Catholicism tries to make for an argument seems to be blatant dishonest use of the scripture.
The implication of papal succession is that by it, it denies faith in 'Christ alone' as sufficient for salvation. This is actually a rejection of Christ and his only catholic church invisible.
Often the biggest argument against something is that there is no supporting argument for it. The scripture gives tradition no real respect, for it affirms that it was by the tradition of the church that the Jews found reason to reject Christ. This argument, absence of teaching denies its truth, is only reasonable when the subject has significant impact on church life and would essentially imply God was irresponsible not to inform his children of such an essential matter through scripture. Scripture is what confirms if any tradition should be upheld or condemned. As papal succession is such an important doctrine, which the actual salvation of souls does depend, and which is possibly the most central teaching of Catholicism, has absolutely no mention of in the scripture, immediately points to its obvious and most critical error. It is from this ground that many Protestant theologians think of the Catholic external organization as a systematic form of an anti-Christ, if not the anti- Christ for its chief aim is at replacing Christ with a visible church and transferring the authority of Christ to the Pope.
This one point for most Protestants actually ends the investigation and is sufficient for its full dismissal with full prejudice. However, there are some further points that may be considered from the biblical context.
Leaving the obvious error of this teaching we turn to God's word for what is a Christian:
- The single definition within the scripture that determines if a visible person should be considered part of the invisible church, is their sincere confession of faith in 'Christ alone' for the forgiveness of their sins. There visible membership to a church organization counts is merely dust on the scales.
because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and is justified, and with the mouth one confesses and is saved. For the Scripture says, “Everyone who believes in him will not be put to shame.” For there is no distinction between Jew and Greek; for the same Lord is Lord of all, bestowing his riches on all who call on him. For “everyone who calls on the name of the Lord will be saved.” (Romans 10:9-13, ESV)
Under the error of papal succession the scripture is grossly and blasphemously perverted into saying, 'whoever believes in Christ...and [put your idol here]. The idol in this case is respect of the physical organization of the papacy. With the second idol, post initiation, as possibly the worship of Mary.
A man's own personal faith directly in Christ and not directly Christ’s ministers or institutions, is the basis of all genuine faith in God. Therefore faith in Christ has the implication of putting all believers under a duty of condemning anyone who preaches a different faith, that is 'faith AND' [put your idol here]. Even if it if an apostle, Pope, or even an angel of God:
But even if we or an angel from heaven should preach to you a gospel contrary to the one we preached to you, let him be accursed. As we have said before, so now I say again: If anyone is preaching to you a gospel contrary to the one you received, let him be accursed. (Galatians 1:8-9, ESV)
Therefore the authority of the Apostles was not physically held by them so that they could pass it on, rather their authority was in proclaiming Christ AND NOTHING. If they, Peter, Paul, or whoever no longer preached this, they were to be absolutely condemned.
The result with respect to papal succession was the reformation largely lead by Martin Luther. This is how the invisible church was restored to the authority of Christ under his word.
It is on the foundational doctrine of Christ, that he will build his church upon himself as the rock, not upon the pope and his pretenders, which Peter’s confession is to be understood. Peter's faith in Christ alone, just as any believers was a 'little rock' upon which all believers are built into the temple of God. This temple is built on this precise gospel teaching that was laid by the Apostles. It here that Protestants and Catholics divide as far as the east of from the west. Papal succession seizes on the potential confusion that the English translation of this Greek sentence and tries to create an idol out of Peter which will an anchor and protect all their pretended authority over every other Christian body of believers.