What does 1 Corinthians 6:4 mean?
Paul is addressing a group of Christians: the church in Corinth. He has identified a root problem for them, born out of their wealth and self-reliance. They are proud and arrogant. That has led them to become divided into factions and to ignore serious sin among them (1 Corinthians 1:11–12; 5:1–2).Now Paul is addressing another result of their selfishness: in at least one case, a member of the congregation has taken another to a secular Roman court over a minor dispute. Paul has made clear that believers ought to be capable of settling such disputes within the church. There is no legitimate reason for brothers and sisters in Christ to submit minor issues to the judgment of unspiritual people (1 Corinthians 2:14–15). Instead of taking trivial matters to those who are not in Christ, such disputes ought to be settled "in-house" among fellow Christians. Paul will write in the following verse that the Corinthians should be ashamed of making this mistake.
Does this mean no Christian should ever sue another, for any reason? Some Bible teachers have reached this conclusion. Most, however, take Paul's reference to "trivial cases" (1 Corinthians 6:2) to imply that secular courts ought only be used as a last resort. In extreme cases, or where one party or the other is living in open rebellion against Christ, involvement of government and secular court might be justified.
Whatever the issue was in this civil case in Corinth, Paul insists that both parties and the rest of the church should have been able to resolve it together instead of taking it outside the church to pagan, un-spiritual Roman judges.