1 Corinthians 6:5

I speak to your shame. Is it so, that there is not a wise man among you? no, not one that shall be able to judge between his brethren? KJV

Then: Culture of the day detested airing family problems in public. You didn't take brotherly disputes into the Roman courts. Paul thinks that the church family should practice the same kind of honor. Keep the disputes private (Hayes, p. 95 and Baker, p. 89). It was beyond shameful that Paul even had to tell them. He follows up with another dig at elitist attitudes. Anybody who is really smart and wise can find amicable ways to resolve petty squabbles.

Now: There are always going to be some poeple who think they are smarter than others. The attitude causes difficulties at both ends. Those scorned must learn endurance, while the lordly must learn humility. Both traits are learned through trial and prayer. Paul's admonitions may occasionally apply specifically, but more often need identification in other situations.

Extra source: First Corinthians by Richard B. Hayes (John Knox Press, 1997) on line at http://books.google.com/books?id=M_PC0PAs3VYC&dq=1+Corinthians+and+Richard+B.+Hays&printsec=frontcover&source=in&hl=en&ei=2oPcStDCIIvf8Aaq0Ki3BQ&sa=X&oi=book_result&ct=result&resnum=11&ved=0CCMQ6AEwCg#v=onepage&q=1%20Corinthians%20and%20Richard%20B.%20Hays&f=false
Cornerstone Biblical Commentary 1 Corinthians (William Baker), 2 Corinthians (Ralph Martin & Carl Toney), ed. by Philip Comfort. Carol Stream: Tyndale House Publishers, c2006.