In Chapter 10, Earle Cairns starts to chronicle the rise of the Roman bishop in order to unify the church in persecution.
As the years passed, the church started with Bishops and Elders for leadership. Elders were over one congregation, and bishops covered a whole region. Soon, five bishops rose in preeminence. Jerusalem, Ephesus, I think Alexandria, somebody else, and of course Rome.
Why Rome? Peter and Paul were martyred there. Persecution was concentrated in Rome. Paul's longest letter was to Rome. Rome had a big role in Church history.
And since Peter died in Rome, people assumed that the Bishop of Rome sat in succession from Peter. They believed this because Jesus in Matthew 16 gave him the keys of the kingdom and said he would build his church in "this Rock." Many people did not have access to the Scriptures at this time to double check the text and had to rely on the Bishops for interpretation.
Clement, Ignatius, and other writers all proposed Church unity by looking toward the Bishop for leadership. The Church needed that at the time. They stayed together and started calling themselves "Catholic" meaning universal church. Some how, all the other prominent bishoprics fell, and Rome still stood.
Sadly, the Roman bishop did not teach the true Rock on which Christ built the church: not Peter, but what Peter said in confessing Jesus as the Christ, the Son of the Living God. Now the focus was on the human hierarchical leadership rather than unity in the Lord and what he said and did.
And since there was only one denomination, it's easy to pick on these people because of their fascination with one geographical location. However, we Americans are no different. We place our faith not in the Bible, but in the Constitution, which is valid, but it's not the unchanging and living Word of God. America is somehow God's favored country, and we must respect our branches of government. No matter who great any nation on earth becomes, no nation will be our eternal home in God's Kingdom, and no person will be the head of the Church other than Christ. He can place regents on earth to govern while we still wait for his return, but God shares his throne with no one.