In order to understand what Paul was teaching, you need to understand the context. What was the situation in Corinth? Why did Paul need to rebuke them initially? Was Paul really suggesting that the Church ignore society? Why did he write again? After all, there are two letters to the Church in Corinth, not just one quote. Two full letters of teaching, and correcting. It's a dangerous thing to pick a quote and think you know to who and about what Paul was teaching.
Back to the point. Yes, we are called to enlighten the culture to the truth of the Gospel! And sometimes, the message does need an edge -- think Jesus in the temple courtyard and when He casts out demons, and even the statements to eat true flesh and drink true blood or have no life within you from the Sermon on the Mount. Fraternal correction -- especially about sexual morality -- isn't always comfortable. And I just can't stomach being corrected so politely and inaccurately with information taken out of context and and argument built upon personal opinion. (Oh, how I despise proof texting!)
Defending the truth -- sharing the Gospel -- doesn't have to be a nasty ordeal, but it does have to remind the sinner to go and sin no more!
Most often, that sinner is us! And I know what I would do if I tried to convince myself to just be a good example instead of mortifying the body and rebuking the intellect that would continue to sin on the inside, but try to be a loving example on the outside. Read 2 Tim 1 and see how Paul in prison counsels Timothy on the preaching of the Gospel; and, as I mentioned above, what does Paul actually say in 1 Corinthians, and then in 2 Corinthians?
My advice to the author:
Knowing who to correct and how to correct in a way that will be heard and understood is a grace. Know your audience -- that's what Jesus did by dining with sinners -- and recognize that the audience in most cases is YOU -- so, start by pulling that plank in your own eye, pray and ask God the best way to reach those in society to whom we are called to evangelize. It begins with self-knowledge and self discipline to better know how to love and serve God and neighbor. Our neighbor doesn't exist only inside the Church!
Let's start here:
"O Eternal Father, I accuse myself before You, in order that You may punish me for my sins in this finite life, and, inasmuch as my sins are the cause of the sufferings which my neighbor must endure, I implore You, in Your kindness, to punish them in my person." (from the Dialogue of St. Catherine of Siena)