In 1 Timothy 3:6-7 Paul begins to deal with the sorts of false teachers who are present in Ephesus. These are the people Timothy was sent to deal with, so it is strange that Paul would say “have nothing to do with these people.” Paul is not describing generic sinful people, rather these are people in the churches in Ephesus who are in a state of rebellion against the scripture and are behaving in ways that deny the power of godliness. Compare this to Paul’s speech to the Ephesian elders in Acts 20:29-30.
The impression here is of a group of (perhaps) wealthy patrons of local elders. They are married (the false teachers sneak into the household), and are perhaps older, with more free time to play the patron for philosophers or teachers. This did occur in the ancient world, perhaps these women are treating Christian teachers in the same way they might treat a Greco-Roman philosopher.
Paul uses an fairly obscure analogy for the false teachers in Ephesus, Jannes and Jambres (verses 8-9). These names do not appear in the Hebrew Bible, but according to both Jewish and Christian tradition, these are the names of the two magicians who opposed Moses in Ex 7:11, 9:11. Jannes is mentioned in the Damascus Document 5:18, both appear in Targum Pseudo-Jonathan on Ex 7:11. Origen, Against Celsus 4.51 claims there is a (now lost) work describing the two men, although the spelling of the name varies. Citing legendary bad examples in comparison to the opponents to the gospel is not unique to Paul. Both 2 Peter and Jude list a series of bad examples in order to describe their own opponents. In this case the emphasis is likely on their opposition to the truth rather than on their use of occult.
That the false teachers are opposing the truth is called folly, and like Jannes and Jambres, they will not be able to stand up to the truth in the end. Is this name-calling? Not really, it is an argument from analogy. Since the false teachers in Ephesus are “foolish” in a biblical sense, they cannot overcome the truth. Can this strategy be used to deal with the sorts of “false doctrine” we encounter today?