Why did Paul not regret making the Corinthians sorry with his first letter?
The correction had to be done, so Paul did not repent or regret the sorrow his letter caused. He had to address the Corinthian problems, and even though the letter made them sorry, he stood by the necessary rebuke rather than reversing it.
Les explains that Paul, writing from Ephesus while Titus was at Corinth, had sent the first Corinthian letter to address their problems and had to dress them down severely. He later heard reports from Corinth that were against him and condemned him, but Titus brought good news: the Corinthians still loved and esteemed Paul. That report thrilled Paul and made him rejoice all the more. In verse 8 he says that even though he made them sorry with a letter, he does not repent or regret it, because it had to be done. The sorrow was tied to necessary correction, not something Paul wished to undo.
For though I made you sorry with a letter, I do not repent, though I did repent: for I perceive that the same epistle hath made you sorry, though it were but for a season.