What does 1 Corinthians 6:1 mean?

Paul launches into a new example of the pride and arrogance of the Christians in the church at Corinth. Apparently, at least one of them had sued another member of the church in a secular, civil court over some disagreement. Paul is outraged over this.

Participating in competitive lawsuits was a common and frequent practice in that era. It was not always a fair one. The wealthy or well-connected in the community had an advantage over others. Bribery of judges and jurors was common. In almost all cases, the two parties would attack each other's character as well as arguing for the rightness of their position. Inevitably, those suing and being sued would become social enemies.

The following verses show that Paul considers it a tragedy that fellow believers in Christ would put themselves in such a position. It's shameful for brothers and sisters in Christ to appeal to unrighteous, non-believing judges instead of fellow born-again Christians.

Paul's use of the term "unrighteous" here has two implications. Primarily, he means these secular authorities are not Christians and have not been made righteous by the blood of Christ. In many cases, these Roman judges were also corrupt, and part of the rampant unfairness associated with civil courts of the day. Paul, himself, had been dragged, literally, before a court in Corinth by the Jewish religious leaders (Acts 18:12–17). That turned out better for him than most of his appearances before Roman judges did.

Paul is not teaching that a Christian should never submit to the authority of a human court. He teaches the opposite of that in Romans 13:1. Christians live under the laws of the land. These verses are about a civil lawsuit, not a criminal case. Nor does he mean Christians can never, under any circumstances, go to court against a person claiming to be a believer—his remark about "trivial cases" in the next verse implies that some issues might need the involvement of a court. For example, if a church member or official is involved in abuse or criminal activity, those actions are absolutely not "protected" by this admonition.