I just summed up what St. Paul himself says in that very chapter–the start of which addresses his letter to the Church in Corinth (being a Church, they would already be baptized for the most part) and then he describes the issue he wants to avoid:
1 Cor. 1:10 I appeal to you, brethren, by the name of our Lord Jesus Christ, that all of you agree and that there be no dissensions among you, but that you be united in the same mind and the same judgment. 11 For it has been reported to me by Chlo′e’s people that there is quarreling among you, my brethren. 12 What I mean is that each one of you says, “I belong to Paul,” or “I belong to Apol′los,” or “I belong to Cephas,”[c] or “I belong to Christ.” 13 Is Christ divided? Was Paul crucified for you? Or were you baptized in the name of Paul? 14 I am thankful[d] that I baptized none of you except Crispus and Ga′ius; 15 lest any one should say that you were baptized in my name. 16 (I did baptize also the household of Steph′anas. Beyond that, I do not know whether I baptized any one else.) 17 For Christ did not send me to baptize but to preach the gospel, and not with eloquent wisdom, lest the cross of Christ be emptied of its power.