I have not found any commentators who directly mention that the Corinthians rejected Paul's recommendations or teaching, rather only that they rejected his style. Colin Kruse in the Tyndale NT Commentaries says:
In this central section of the letter Paul appeals to the Corinthians to be reconciled to God and open their hearts to their apostle. He clears the grounds for these appeals by first responding to criticisms of the style of his ministry (5:11-15), and then stating the theological basis upon which reconciliation rests (5:16-21).
And possibly the ESV Study Bible's notes by Scott J. Hafemann on 2 Corinthians 5:13:
This probably responds to Corinthian mockery of Paul as crazy;
The rejection or derision of Paul would likely include rejection of his recommendations, and so the necessity of responding to criticisms before making further recommendations to the church in Corinth.