Throughout history, many Christian groups claimed, and continue to this day to claim, authority from the Apostles. Most famous among these groups are the Catholic and Orthodox Churches, both of which claim Apostolic Succession as a basis for their authority. But what these two groups, and those who follow them, fail to realise is that this claim is entirely baseless.
The first problem with it is that Apostolic Succession is a completely fictitious concept. Throughout scripture, you will find no reference to it, nor even indication that the authority of an Apostle is transferrable. By contrast, there is very strong evidence that it isn't. Indeed, the very definition of the word "Apostle" precludes the possibility.
The word "Apostle" means "one who is sent out". This term was actually used outside the Church as well. A person given the authority to speak on behalf of the Roman Emperor, for example, was considered his Apostle. There are a few senses in which this can apply in a Christian context, but most relevant to those who seek to claim Apostolic authority is those who were sent out by God. The 12, along with Paul, are the obvious examples. Jesus chose the 12 (Mark 3:16-19), and of course Paul too (e.g. Romans 1:1-2). A major problem with claiming to be in the same league as these men is that, aside from the fact they never claimed they would pass down their authority, no one could claim it in the way they did, nor could they demonstrate their authority as the Apostles did.
During the time of the Apostles, 3 important qualifications were in place for the office of Apostle. These signs were that you had to have seen Christ (1 Corinthians 9:1), you had to be chosen by God (Matthew 10:1-7; Mark 3:14; Acts 1:24-26, 9:15; Galatians 1:1), and you had to be able to demonstrate your right to be an Apostle with "the signs of a true Apostle", i.e. miracles (2 Corinthians 12:12). Without weighing in on the controversy over whether or not Matthias was a "wrong choice", at least the first two of these criteria were used by the 11 as a criteria when deciding who would replace (not succeed) Judas.
Paul, especially, blocks the possibility of Apostles following him when he wrote, in 1 Corinthians 15:8-9, "And last of all he was seen of me also, as of one born out of due time. For I am the least of the apostles, that am not meet to be called an apostle, because I persecuted the church of God." If Paul was called "as of one born out of due time", then a later Apostle, of whom we know not, would certainly have been born out of due time.
So, clearly, Apostolic Succession is just out of the question. There is no biblical evidence for it, there is plenty of biblical evidence against it, it's just not a viable thing to claim. Thus, we already have concrete proof that Churches which claim Apostolic authority are apostate, as they have fabricated a revelation from God. "...such are false apostles, deceitful workers, transforming themselves into the apostles of Christ. And no marvel; for Satan himself is transformed into an angel of light. Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works." (2 Corinthians 11:13-15).
But let's suppose Apostolic Succession was a thing. If a man could inherit the office of Apostle, what would he be inheriting? Such a man would only be a steward of the mysteries of God (1 Corinthians 4:1), able to reveal scripture (Galatians 1:11-12; 2 Peter 3:15-16), but completely subservient to it (Galatians 1:8), and even able to be tested against it by those with less authority (Psalm 119:97-100, 130; Acts 17:11).
So we see, far from having the authority to alter the Christian faith (which Jude 1:3 tells us was once for all delivered to the saints, meaning we shouldn't expect it to change anyway), the Apostles acted as servants to God. They did not even expect to be infallible. They believed they would be judged, even more harshly than those in lesser office (James 3:1), and would even rebuke each other on matters of faith (Galatians 11:2-14). Especially relevant to fake Apostles such as the Pope is who was doing the rebuking. Paul, who by his own confession was least worthy to be an Apostle, rebuked Peter, who First Vatican Council made the mistake of claiming was "in his single person, preferably to all the other Apostles, whether taken separately or together". Yet, biblically speaking, Peter was not even remotely papal. Ironically, it would have been smarter (though of course still false) for Catholics to tie the papacy to Paul.
But moving on from the abomination that is the Papacy, is it possible that information has been transmitted through some Church or other that we wouldn't otherwise have? Some oral tradition, for example, that might change the way we understand the scriptures? Such an attitude was considered heretical even among the very people Apostolic Churches so often appeal to. Irenaeus, for example, wrote "When, however, they are confuted from the Scriptures, they turn round and accuse these same Scriptures, as if they were not correct, nor of authority, and [assert] that they are ambiguous, and that the truth cannot be extracted from them by those who are ignorant of tradition. For [they allege] that the truth was not delivered by means of written documents, but by word of mouth." (Irenaeus, Against Heresies).
In reality, while the Apostles did preach orally, they preached the same things as can be found in the scriptures (e.g. Acts 15:27). It is absurd to believe that the Apostles would have contradicted the scriptures, particularly their own writings, especially given the very harsh pronouncement found in Galatians 1:8. "But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed." (emphasis added). Their teachings were consistent throughout their entire ministry, which is shown even more powerfully by the consistency of each book of the New Testament.
These, by the way, were often written to correct some very major errors in the early Church, which happened even while the Apostles were still alive to deliver such corrections. Read 1 Corinthians and tell me Paul sounds especially pleased with the Corinthian church. Read Galatians, you'll be even more shocked. In fact, the very way in which Paul opens Galatians seems to indicate they may be Apostate.
In our modern world, "church" is used in a uniquely Christian manner. Historically, however, it merely meant "assembly". Or rather, Ekklesia, the word translated as "Church", did. We see an example of this in Acts 19:21-41, in which some rioters who worshipped a goddess called Diana, are called "Ekklesia". Thus, Paul is unique in that in most of His Epistles, with Galatians being the sole exception, begin by identifying the recipients' "churches" with God. Observe:
Paul, a servant of Jesus Christ, called to be an apostle, separated unto the gospel of God, (...) To all that be in Rome, beloved of God, called to be saints: Grace to you and peace from God our Father, and the Lord Jesus Christ. - Romans 1:1, 7, emphasis added
Paul called to be an apostle of Jesus Christ through the will of God, and Sosthenes our brother, Unto the church of God which is at Corinth, to them that are sanctified in Christ Jesus, called to be saints, with all that in every place call upon the name of Jesus Christ our Lord, both their's and our's: - 1 Corinthians 1:1-2, emphasis added
Paul, an apostle of Jesus Christ by the will of God, and Timothy our brother, unto the church of God which is at Corinth, with all the saints which are in all Achaia: - 2 Corinthians 1:1, emphasis mine
Paul, an apostle of Jesus Christ by the will of God, to the saints which are at Ephesus, and to the faithful in Christ Jesus: - Ephesians 1:1, emphasis mine
Paul and Timotheus, the servants of Jesus Christ, to all the saints in Christ Jesus which are at Philippi, with the bishops and deacons: - Philippians 1:1, emphasis mine
Paul, an apostle of Jesus Christ by the will of God, and Timotheus our brother, To the saints and faithful brethren in Christ which are at Colosse: Grace be unto you, and peace, from God our Father and the Lord Jesus Christ. - Colossians 1:1-2, emphasis mine
Paul, and Silvanus, and Timotheus, unto the church of the Thessalonians which is in God the Father and in the Lord Jesus Christ: Grace be unto you, and peace, from God our Father, and the Lord Jesus Christ. - 1 Thessalonians 1:1, emphasis mine
Paul, and Silvanus, and Timotheus, unto the church of the Thessalonians in God our Father and the Lord Jesus Christ: - 2 Thessalonians 1:1, emphasis mine
Note how in every Epistle to a church or group of Christians, Paul links the recipients to God in some way. He may say "to the church of God", or "to the saints in this location", or "to the church which is in God the Father and in the Lord Jesus Christ". Now read his greeting to the Galatians:
"Paul, an apostle, (not of men, neither by man, but by Jesus Christ, and God the Father, who raised him from the dead;) And all the brethren which are with me, unto the churches of Galatia: Grace be to you and peace from God the Father, and from our Lord Jesus Christ, Who gave himself for our sins, that he might deliver us from this present evil world, according to the will of God and our Father: To whom be glory for ever and ever. Amen." (Galatians 1:1-5).
Notice how at no point during his greeting does Paul attempt to link "the churches of Galatia" with belonging to God. Even within the same chapter, Paul seems to make further distinction between the "churches of Galatia" and Christian churches. While he doesn't dignify the churches of Galatia with any kind of Christian titles, he does so with the Churches of Judea "...which were in Christ" in verse 22.
To show that this is not my opinion, consider the following commentary from Heinrich August Wilhelm Meyer: "The relations of the churches were different in Achaia: see on 1 Corinthians 1:2 ; 2 Corinthians 1:1 . The fact that Paul adds no epithet of honour (as κλητοῖς ἁγίοις , or the like) is considered by Chrysostom, Theophylact, Oecumenius, and by Winer, Credner, Olshausen (comp. Rückert), Hilgenfeld, Wieseler, a sign of indignation. Comp. Grotius, “quia coeperant ab evangelio declinare.” And justly so; because it is in keeping with the displeasure and chagrin which induce him afterwards to refrain from all such favourable testimony as he elsewhere usually bears to the Christian behaviour of his readers, and, on the contrary, to begin at once with blame (Galatians 1:6 ). In no other epistle, not even in the two earliest, 1 and 2 Thess., has he put the address so barely, and so unaccompanied by any complimentary recognition, as in this; it is not sufficient, therefore, to appeal to the earlier and later “usage of the apostle” (Hofmann)."
Now, is this view correct? Did Paul genuinely alter his posture towards the Galatians in order to show that he did not consider them Christian? In truth, I'm not sure, and so I'll simply leave Meyer's opinion (which does seem well attested) out in the open to be picked up by those to whom it seems reasonable. However, while I am not firmly convinced to share this opinion, it does fit very well with the context of his epistle to the Galatians. As Meyer said, Paul does indeed begin immediately with blame. Following his greeting, Paul writes "I marvel that ye are so soon removed from him that called you into the grace of Christ unto another gospel: Which is not another; but there be some that trouble you, and would pervert the gospel of Christ." (Galatians 1:6-7).
And this, of course, is where Paul effectively threatens himself and the other Apostles with "let them be anathema". He even later tells them "Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace." (Galatians 5:4, emphasis mine). Christ is of no effect? The Galatians have fallen from grace? If Paul's frosty greeting does not tell us the Galatians are Apostate, phrases like this should certainly indicate they are not truly Christian.
Now, I find myself heavily conflicted with this. On the one hand, Paul rebukes them for accepting another gospel (i.e. a fake one), and tells them Christ is of no effect to them and they've fallen from grace. On the other hand, he calls them brothers (e.g. Galatians 6:1), and of course has taken the time to write to them in the first place, suggesting to me that they are certainly not beyond redemption, and may only be flirting with the fake gospel. Of course, if faith comes by hearing, and hearing by the word of God (Romans 10:17), I have little doubt that Paul's epistle was a major wake up call to most of those within these assemblies of Galatia. God knows how to keep His saints. Nevertheless, all of this shows that even entire congregations can stray from the truth.
What's worse is that even the best of churches are vulnerable to snakes. In Acts 20:29-30, Paul warns the elders of the Church of Ephesus "...I know this, that after my departure savage wolves will come in among you, not sparing the flock. Also from among yourselves men will rise up, speaking perverse things, to draw away the disciples after themselves. Therefore watch, and remember that for three years I did not cease to warn everyone night and day with tears."
This is one reason God would never establish such a reckless doctrine as Apostolic Succession. Just as the kings of Israel would sometimes be good, and sometimes be bad, it is only human nature that any successors of the Apostles could be perverse apostates. By leaving us with His own infallible word, God not only left us the actual authority of the Apostles, but prevented Satan from usurping it, at least for His saints, who hear His voice. Imagine a religion in which those savage wolves could never be challenged by the flock. How detestable would a faith become if when men rose up, speaking perverse things in order to draw away the disciples after themselves, we were commanded to let them?
From all of this, we see the precarious position the saints are actually in. Satan can never overcome the Church, but God has certainly given him power to try. And so we see that even while the Apostles, God's chosen vessels to carry the Gospel to the world, were doing just that, even the churches they personally set up fell into disarray. Their worship practices got messed up, their doctrines needed correcting, even their moral behavior was unfitting for the Church. And so a question to ponder is that if the churches of the Apostolic Age were so capable of falling into error, skirting the edge of apostasy, and even producing false teachers, how much more can modern Churches, 2,000 years later, fall prey to Satan's schemes?
More importantly, what can the saints do about it? When preachers come to us claiming to have Apostles in their Churches, what are we to make of them? First of all, remember this: Just by virtue of usurping an office that has been closed since the end of the first century, they are to be considered heretical. But more than that, we do have Apostolic authority, greater authority even than that, and with the increase in information technology, it is now available to us at the click of a button. We have the very writings of the Apostles, and their predecessors, the prophets, inspired by none other than the Good Lord Himself (2 Timothy 3:16-17). Therefore, if any serpent dares to call himself an Apostle, every false claim that comes out of his mouth can be tested against scripture and broken like a bread stick in a blender. Only one Church, the Church of God on the Earth, has Apostolic authority, and it is not a Church with a denominational name.