They were puffed up and proud rather than humbled and mourning because of the sin.
The sin should be judged. God’s people should be more concerned about obeying Him and about preserving His testimony than about the feelings of any one person or group of persons.
It was to be done by the church (1 Cor. 5:4, “when ye are gathered together”). Even Paul the apostle did not exercise this discipline himself. It was to be done by the church. There is no higher body of appeal in the New Testament dispensation than the assembly. It is the “pillar and ground of the truth” (1 Tim. 3:15). Denominational practices of establishing headquarters and committees and judicial bodies outside of the church and to which the church must appeal its decisions are unscriptural and destructive to the work of Christ. The New Testament assembly has the authority to ordain its own pastors (Acts 14:23), to send out its own missionaries (Acts 13:1-4), and to carry out its own discipline (1 Cor. 5).
Church discipline is for their testimony’s sake. The church must maintain a good testimony before the unbelieving community (1 Cor. 5:1). The matter was common knowledge in the church and doubtless in the community, as well. The church bears the name of Jesus Christ and represents Christ in this world. It is the light that the world sees, and if the light is corrupted by open and grave sin, the world will be offended at Christ. Compare Ph. 2:14-15; 1 Pet. 2:9-12.
Note: Paul seems to mention here a previous letter that he had written to the church at Corinth. Together with many other of his epistles, this first one to Corinth has perished and we know nothing about it beyond this brief mention. God chose which of the apostolic epistles were to be divinely inspired and canonized and preserved, and those that He chose are all that we need (2 Tim. 3:16-17). (Some commentators believe that Paul was referring here to an earlier portion of this same epistle, though we do not accept this view.)
God’s people must be careful to maintain the proper attitude when dealing with sinning Christians and not to give the Devil a place.