How is 1 Corinthians 1:10-13 understood by proponents of the primacy of Peter?

Question

Now I beseech you, brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing, and that there be no divisions among you; but that ye be perfectly joined together in the same mind and in the same judgment. For it hath been declared unto me of you, my brethren, by them which are of the house of Chloe, that there are contentions among you. Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ. Is Christ divided? Was Paul crucified for you? Or were ye baptized in the name of Paul? - 1 Corinthians 1:10-13

It is certain that Cephas, here, is the Apostle Peter (John 1:42). In Paul's chastisement of the Corinthian believer's "contentions" he lists 4 names that they are claiming to be "of". He outright eliminates himself from the list but, if he recommends any name on the list, it is not Cephas (Peter) but Christ. A natural reading of verse 13 looks like this: Is Christ divided? Was Paul (or Apollos or Cephas) crucified for you? or were you baptized in the name of Paul (or Apollos or Cephas)?

How do proponents of the primacy of Peter reckon with Paul apparently placing Peter and Apollos on equal footing here? Why does Paul give no hint of any special status for Peter over either himself or Apollos when attempting to correct divisions in the Church?

Answer 1

How is 1 Corinthians 1:10-13 understood by proponents of the primacy of Peter?

St. Paul was merely expressing the fact that division of some sort had existed in Corinth. He does not really go into details here other than acknowledging the fact that some seem to have favourites and prefer to be known as a follower of one apostle over another. St. Paul is simply trying to stop this notion from continuing.

A Church Divided Over Leaders

10 I appeal to you, brothers and sisters, in the name of our Lord Jesus Christ, that all of you agree with one another in what you say and that there be no divisions among you, but that you be perfectly united in mind and thought.

11 My brothers and sisters, some from Chloe’s household have informed me that there are quarrels among you.

12 What I mean is this: One of you says, “I follow Paul”; another, “I follow Apollos”; another, “I follow Cephas”; still another, “I follow Christ.”

13 Is Christ divided? Was Paul crucified for you? Were you baptized in the name of Paul? - 1 Corinthians 1:10-13

I truly do not see St. Paul making an argument here for or against the Primacy of St. Peter, called Cephas (Rock). This passage of Sacred Scripture is simply trying to maintain Christian unity within the Early Church.

Please read the entire text.