I imagine there were probably plenty of well-meaning, sensitive, tolerant types in the Church at Corinth who criticized the Apostle Paul with some simple-minded misapplication of the “Judge not lest ye be judged” quote from Jesus a half century earlier. Not only did Paul point out a plethora of problems; i.e. abuses, doctrinal errors, schisms, and even a case of gross, incestual sin, but he did it with a PUBLIC LETTER. Surely, they must have argued that he should have confronted those sinning members personally and privately according to Jesus' instructions, rather than bringing “harm to the Body of Christ.”
But the real problem was that their sins were not private; they were public and the Church needed to be straightened out. In the case of incest, the sin was commonly known among them. The real outrage was that they were tolerant of it. They all knew about it including their own leaders and, as is typical today, they did nothing to correct it or judge it. It took an outsider to confront them with it.
Paul’s letter did NOT harm the Body. In his second letter, we read where he commended them for their godly sorrow, which led to repentance, and the result was that the Church was corrected, cleansed and strengthened.