Some Ways To Argue Against A Papacy

It's useful to think of ways to concisely address a subject. That helps when we don't have much time in a particular context or we're looking for brief way to start a conversation on the topic, for example. In a post a few years ago, I summarized nine lines of evidence to consider when evaluating the papacy:

Regarding the evidence against the papacy outside of Matthew 16, think of the many contexts in which a papacy could have been mentioned early on, but wasn't: there's no reference to a title for a papal office (in contrast to "apostle", "deacon", etc.); the qualifications for holding other offices, like apostle and elder, are mentioned in places like Acts 1 and 1 Timothy 3, whereas there's no such discussion of the qualifications for being a Pope; passages discussing the structure of the church, like 1 Corinthians 12 and Ephesians 4, say nothing of a papacy; the imagery used for the church in Ephesians 2 and elsewhere doesn't make any effort to portray a papal office; the imagery used for the apostles in Matthew 19 and elsewhere (e.g., twelve thrones, twelve foundation stones) doesn't make any effort to portray a papal office; in passages in which the apostles are anticipating their departure in some sense (Paul departing from the Ephesian elders in Acts 20, Paul and Peter anticipating their deaths in 2 Timothy and 2 Peter), there's no reference to a papal office, looking to the bishop of Rome as the foundation of the church, looking to the bishop of Rome as the center of Christian unity, or anything like that; the earliest sources to comment on the Roman church and its importance (Paul in Romans, Luke at the end of Acts, Ignatius, Dionysius of Corinth, Irenaeus, etc.) give a variety of non-papal reasons for the Roman church's significance; the early opponents of Christianity, including ones who addressed the religion at as much length as Trypho and Celsus did, showed no awareness of a papacy. Furthermore, passages like 1 Corinthians 12:28 (mentioning "apostles" as the first order in the church) and Galatians 2:9 (grouping Peter with other apostles and naming him second) make more sense if there was no early belief in a papacy than if there was a belief in it.

Some of the arguments don't have enough significance to use in isolation. They should be part of a cumulative case instead. But some of them could be used in isolation. You could choose one or more to start with, then move on to others if warranted.