In these passages Paul greets the Corinthian believers, those who had been sanctified in Christ Jesus. He expresses his thankfulness for them. However, Paul also criticizes them for quarrels among them caused by split loyalties: some to Peter, some to Paul, some to Apollos and some to Jesus Christ.
Paul chastises them for their split loyalty. He tells them that their loyalty should be only be to Jesus. Paul points out that only Jesus was crucified for them: not Paul, Peter, or Apollos.
We see this tendency today in religion where some people put their devotion and confidence on church leaders rather than Jesus Christ. This is most evident in the Catholic Church where some people worship the Pope.
We must never forget the reason we are Christians. It was Jesus who died for us so that our sins could be forgiven. We must never place our adoration or worship on a priest or religious leader. Our focus must always be on Jesus Christ.