In 1 Corinthians, Paul exhorts the believers in Corinth to unity:
I appeal to you, brothers, by the name of our Lord Jesus Christ, that all of you agree and that there be no divisions among you, but that you be united in the same mind and the same judgment. For it has been reported to me by Chloe’s people that there is quarreling among you, my brothers. What I mean is that each one of you says, “I follow Paul,” or “I follow Apollos,” or “I follow Cephas,” or “I follow Christ.” Is Christ divided? Was Paul crucified for you? Or were you baptized in the name of Paul? (1 Corinthians 1:10-13 ESV)
In this passage, Paul does not tell us exactly what the nature of the division is. We don’t know what caused the divisions. (Although, there may be some clues in the rest of the letter.)
Here’s the question. When the Corinthians claimed to follow Paul, Apollos, Cephas (Peter), or Christ, were they simply stating their preference for those people, or were they stating their preference for certain doctrinal distinctives represented by those people?