A Note: It is one thing to engage with and argue against the evidence and claims of the Catholic Church. That is a respectable position that opens the door for dialogue. It is another thing entirely to label them unprovable without argumentation, especially as an easy historical case could be made that the burden of proof rest upon the one in protest.
1. Apostolic Succession
Challies quickly inserts his presumptions into his argumentation without offering any evidence. He begins with assumptions, argues with them, and concludes with them. At least he partially understands succession, “Rome claims to trace her lineage in an unbroken line that extends all the way back to the apostle Peter…” He continues, “I do not recognize such lineage and, therefore, do not recognize such authority. Her claims are unprovable and represent a distortion of the Bible’s claims about Christ’s church.” What Mr. Challies, the sola authority, is really saying is, “I disagree with her, therefore she isn’t the church,” exercising a disabled cognitive ascension in differentiating between a subjective and an objective truth. The logic looks akin to, “Since I can’t be convinced of Her claims they are obviously unprovable. If they were provable, I would have to admit I am wrong and She is right. So, She is not the Church. She actually is so much not the Church that She is a false Church, though, I can’t actually identify the true Church. Why? Because R.C. Sproul said so.”
He claims it to be “unprovable” without evidence. So let us provide him with some evidence. “If it is archaeological evidence he wants, he can turn to John Evangelist Walsh’s The Bones of St. Peter, which recounts in detail the excavations under the high altar of St. Peter’s Basilica. If he wants literary or historical proof, he can turn to a reference work such as Jurgen’s The Faith of the Early Fathers, which quotes sixteen passages from early Christian writers attesting to Peter’s being in Rome and dying there. In fact, we have more sources citing Peter’s presence in Rome than we have affirming Caesar’s crossing the Rubicon”.  And if it is proof of succession he desires, the names are listed in any encyclopedia. The second pope “was Linus, as a few moments’ research would have shown”. Challies “made no effort to look at even plainly secular sources (forget Catholic sources) in developing his critique”. 
Jurgen’s The Faith of the Early Fathers, even goes on to quote the Church Fathers in saying, “Peter established his See at Rome and made the Bishop of Rome his successor in the primacy” .
The authoritative role that Peter is given is evident when he receives the keys of the kingdom, after being promised by the Faithful God that the Church would be built upon him. This is the fulfillment of the prophecies in Isaiah 22:20-23; “On that day I will summon my servant Eliakim, son of Hilkiah I will clothe him with your robe, gird him with your sash, confer on him your authority. He shall be a father to the inhabitants of Jerusalem, and to the house of Judah. I will place the key* (Key: symbol of authority; cf. Mt 16:19; Rev 3:7) of the House of David on his shoulder; what he opens, no one will shut, what he shuts, no one will open. I will fix him as a peg in a firm place, a seat of honor for his ancestral house.”
These said servants, typologically point (foreshadow, as in “Adam is a type of Christ”) to Peter as steward of the kingdom. The servant is not the King Himself, but his Vicar.
Near the end of the second century, Irenaeus mentioned that Matthew wrote his Gospel, “while Peter and Paul were evangelizing in Rome and laying the foundation of the Church”. He said the two departed from Rome, perhaps to attend the Council of Jerusalem, and he noted that Linus was named as Peter’s successor – that is, the second Pope – and that next in line were Anacletus (also known as Cletus) and then Clement of Rome. 
…Peter was first in authority among the Apostles. When they were named, Peter almost always headed the list (Mt. 10:1-4; Mk 3:16-19; Lk 6:14-16; Acts 1:13); sometimes it was only ‘Peter and his companions’ (Lk 9:32). Peter was the one who generally spoke for the apostles (Mt 18:21; Mk 8:29; Lk 12:41; Jn 6:69), and he figured in many of the most dramatic scenes (Mt 14:28-32; 17:24; Mk 10:28). On Pentecost it was he who first preached to the crowds (Acts 2:14-40), and he worked the first healing (Acts 3:6-7). And to Peter came the revelation that Gentiles were to be baptized (Acts 10:46-48). 
And sometime after Simon’s new name is given (name changing is certainly not a meaningless gesture in Jewish culture), is he not promised, “Whatever thou shalt bind on earth shall be bound in heaven; whatever thou shalt loose on earth shall be loosed in heaven” (Mt 16:19). “Here Peter was singled out for the authority that provides for the forgiveness of sins and the making of disciplinary rules”.  For where do we go when someone needs disciplined on account of licentiousness? Are they privately summoned before the Bible (which, by historical fact, was not in existence yet), or are they to be summoned before the authority of the Church (Mt 18:15-17)? It is not the Bible that is “the pillar and bulwark of the truth,” but the Church (1 Tim 3:15). Jesus did not institute or promise a book – but a Church.
A quick resource, Peter the Rock, by a former Southern Baptist, who found his way Home to Jesus’ Church. For a thorough examination of the Papacy, see Stephen Ray’s book, Upon this Rock (I’ll buy it for you, firstname.lastname@example.org).
Jesus came to establish One Church, One Body, and One Bride, not 30,000+ denominations; He is not a polygamist. To remove the institution of the visible organic Body from the Head, for an invisible body (bodies aren’t invisible) or “Churchless Christianity,” is to participate in the beheading of Jesus. This is not so in the Catholic Church. We are not a people of a book, like the Muslims. We are a people of a Person. A Person whose body is the Church and whose word is repeated through the ages by that Church in the Holy Writ and Sacred Tradition. The Bible did not slide down a rainbow; it was authoritatively canonized nearly 400 years after Jesus established the Church and gifted to us by the Church councils who themselves received it as custodians, not masters. Which leads us to ask, who was the authority during this time? Sola scriptura, by mere logic, reason, and historical data, holds no weight.
Challies reasons as if, The Lord poured out His Spirit, which will lead us into all truth, at Pentecost, then, He waited 1500 years to bless His “underground Church” with the supreme mediators Luther and Calvin.
Challies maintains he adheres to Protestantism because of R.C. Sproul; I converted to the R.C. Church because of Jesus’ faithful calling, promises, and New Covenant. Challies Christianity is traced to R.C. Sproul, mine, for two millennia back to the Patristic Fathers, The Apostles, and Jesus.
The article does eventually get around to quoting someone (without citation), yet, the subjectivism in no way supports his claim. The quote by, Leonardo De Chirico, places salvation emphasis on “personal relationship with Jesus (nowhere in the Scriptures or Tradition) and reading the Bible (excluding the illiterate and the first 400 years of Christians). This man accepts the New Testament written, compiled, closed, and given to him by the authority of the Church, yet, ironically uses his subjective interpretation of the Bible to reject the Church; how does he not view this as a contradiction of objective truth? The quote further demonstrates Evangelicalism’ inability to define what in fact is an objective Christian.