What does 1 Corinthians 6:6 mean?

Starting in verse 5, Paul seems bewildered that the problem at hand is even happening. He is dismayed that brothers in Christ would choose to take a minor dispute before a secular court, rather than be judged among those who are in Christ (1 Corinthians 2:14–15; 6:1–4).

He doesn't say it outright, but perhaps Paul is also concerned for what such lawsuits will do to Christ's reputation in the culture (1 Peter 2:12). What message does it send to unbelievers, when Christ appears to have made little impact on those who follow Him? How degrading is it to the Holy Spirit to suggest that born-again believers can't resolve a minor dispute among themselves? What kind of ammunition does this give to those who are opposed to the gospel of Jesus to slander the church?

Instead of focusing on that angle, Paul seems most concerned with the hard and indifferent hearts of the Christians in Corinth. By taking each other to court over a trivial matter, they fail to treat each other as brothers and sisters in Christ. In this and other ways, the Corinthians live as those belonging to their culture, more than those who belong to Christ.

The teaching here is not that Christians should not submit to the authority of a secular court. Romans 13:1 teaches believers to submit to the authority of human governments. Also, the concerning event here is not a criminal case or an instance of some gross misconduct. Earlier verses characterized what Paul criticizes as "trivial cases." In civil and minor disagreements, it's shameful for Christians to voluntarily be judged by unbelievers over a minor dispute. Rather, such matters should always be mutually resolved within the church.