Paul learned that certain men within the church were teaching false doctrines. Their probable position as leaders or elders in the church (see introduction and note) called for immediate action. Timothy was to command these individuals not only to stop teaching false doctrine but also to put an end to their speculative system of interpretation.
False doctrines literally means "different doctrines" (compare 6:3), those that diverged from the accepted teaching of the Old Testament, Christ and the apostles. The little we know of the specific content of these teachers' doctrine suggests that its central feature was a misunderstanding about the resurrection of believers (2 Tim 2:18). Perhaps due to some confusion over the Pauline teaching that believers even now participate in the death and resurrection of Christ (Rom 6:4-5, 8; 2 Tim 2:11), they believed and taught that the resurrection of believers had already occurred in a spiritual sense (see further 2 Tim 1:5 and introduction).
That such a mistake could be made may seem strange to us. But the fervency of the first-generation church's hope of Christ's return and certain carryovers from the pagan religions out of which believers came (see comment on 2 Tim 1:5) could have led some to the conclusion that all of salvation's blessings were to be experienced now. A modern parallel is what we might describe as Christian triumphalism (or the "health and wealth" gospel), which tends to present the Christian message as the quick solution to all of life's problems. The same basic mistake seems to be involved. In any case, the heretics' special insight into spiritual matters, which they termed "knowledge" (6:20), also had ethical implications, as allusions to their asceticism would suggest (4:3).