1 Corinthians 1:12

this I say--this is what I mean in saying "contentions" (Co1 1:11). every one of you saith--Ye say severally, "glorying in men" (Co1 1:31; Co1 3:21-22), one, I am of Paul; another, I am of Apollos, &c. Not that they formed definite parties, but they individually betrayed the spirit of party in contentions under the name of different favorite teachers. Paul will not allow himself to be flattered even by those who made his name their party cry, so as to connive at the dishonor thereby done to Christ. These probably were converted under his ministry. Those alleging the name of Apollos, Paul's successor at Corinth (Act 18:24, &c.), were persons attracted by his rhetorical style (probably acquired in Alexandria, Co1 3:6), as contrasted with the "weak bodily presence" and "contemptible speech" of the apostle. Apollos, doubtless, did not willingly foster this spirit of undue preference (Co1 4:6, Co1 4:8); nay, to discourage it, he would not repeat his visit just then (Co1 16:12). I of Cephas--probably Judaizers, who sheltered themselves under the name of Peter, the apostle of the circumcision ("Cephas" is the Hebrew, "Peter" the Greek name; Joh 1:42; Gal 2:11, &c.): the subjects handled in the seventh through ninth chapters were probably suggested as matters of doubt by them. The church there began from the Jewish synagogue, Crispus the chief ruler, and Sosthenes his successor (probably), being converts. Hence some Jewish leaven, though not so much as elsewhere, is traceable (Co2 11:22).

— Jamieson-Fausset-Brown Commentary (public domain)