The opponents in Ephesus stand in contrast to Paul’s record of suffering (v. 13) It is Paul and Timothy’s opponents who are the imposters. The noun (γόης) Paul uses here is a common way to describe an opponent in a philosophical debate. The noun originally referred to a sorcerer (T.Sol 19:3 uses it for a witch, Herodotus, Hist. 7.791.2 for magicians, sometimes it refers to a “juggler,” [Aeschines, Ctes. 137], presumably because they do some sort of distracting act while they pick the pockets of the crowd.).
By the first century this word was used to describe a swindler or a con-man who used some kind of deception to gain a profit from his audience. I think of the character from old Western movies, the “snake oil salesman.” The Greek writer Demosthenes used the word in this sense: “for fear I should mislead and deceive you, calling me an artful speaker, a mountebank, an impostor, and so forth” (Dem., 18 276).
Ironically, these deceivers succeed in deceiving themselves! This is also a common way of describing sophists and charlatans in Greco-Roman world (Dio Chrysostom, Orations, 4.33). The way to avoid these sorts of people is proper “divine” education (4.29).
Dio Chrysostom, Orations 4.33 If, however, he falls in with some ignorant and charlatan sophist, the fellow will wear him out by leading him hither and thither, dragging him now to the east and now to the west and now to the south, not knowing anything himself but merely guessing, after having been led far afield himself long before by impostors like himself.
Similarly, the way to avoid the self-deceptive teaching of the opponents in Ephesus is to devote oneself to divine teaching through the Scripture which has been given by God.
Paul encourages Timothy to “continue in what he has learned” from the Scriptures (vv. 14-15). Timothy was trained in the scripture from a young age. Jewish family, reading the Old Testament in Greek (most likely). While the opponents are progressing into more esoteric “deep” knowledge, Timothy is told to remain where he is. He has already learned the truth and has been convinced that it is the truth. There is no need for him to dabble in the “myths and genealogies” of the opponents.
The Jews regularly referred to their scriptures as “sacred writings,” Paul can only have in mind here the Old Testament. At this point in history it is unlikely that the Gospels were circulating as Scripture, perhaps Paul’s churches cherished his letters as authoritative. But the New Testament as we know it simply does not exist yet!
Paul says Timothy was “raised on the Old Testament.” We know that his mother was Jewish and it is likely that he was taught the Old Testament, perhaps having some training in the Septuagint and Hebrew Bible in a synagogue. I doubt that Paul selected Timothy as a missionary companion if he was totally ignorant of the Bible prior to coming to faith in Jesus!
The remedy for self-deception, for Paul, is an absolute reliance on the Scripture for faith and practice. While the opponents in Ephesus pursue fruitless “myths and genealogies” Timothy is to remember what the Scriptures plainly teach and pursue righteousness.
I suspect if people actually read the Bible, they would not tolerate the sort of “teaching” that passes for popular Christian preaching!