Christians Are Not To Go To Court Against Their Fellow-Christians (6:1-9a).
The idea that the church judges internal matters like sin leads on to the idea that the church can also act as judge in disputes. The general principle behind this passage is that Christians should be able to sort out matters between themselves and not resort to local civil judges in the market place or to civil law courts. By doing do they encouraged the mockery of non-Christians. But Paul's main concern is probably really with the failure of Christians to follow Christ's injunctions (Matthew 5:23-26; Matthew 5:38-41) and their failure to love one another (John 13:34; John 15:12; John 15:17; Romans 13:8; 1Th 4:9; 1 Peter 1:22; 1 John 3:11; 1Jn 3:23; 1 John 4:4; 1 John 4:11-12). Such things should be dealt with internally.
In Paul's day one danger was that in going to a pagan court the Christians drew attention to themselves, especially where the dispute might be related to Christian matters, and that they did it in front of courts which were based on submission to the Emperor of Rome, which were not always favourable towards Christians. Thus when times of trouble came they and their affairs were known to the courts and in the public domain and thus more easily attacked. But there is also the principle that for Christians to reveal unchristian aims and behaviour before non-Christians (for usually one side must be in the wrong, or both be partly in the wrong) is to be a bad witness, especially where they were brought out into the open before the judgment seats in the marketplaces before crowds of ordinary people. Dirty Christian linen should not be washed in public.