The first full paragraph of the letter works to answer a very important question for the purpose of Paul’s correspondence with Timothy: Why must Timothy continue to work to silence the false teachers?
As I urged you when I went into Macedonia, stay there in Ephesus so that you may command certain men not to teach false doctrines any longer nor to devote themselves to myths and endless genealogies. These promote controversies rather than God's work-- which is by faith. The goal of this command is love, which comes from a pure heart and a good conscience and a sincere faith. Some have wandered away from these and turned to meaningless talk. They want to be teachers of the law, but they do not know what they are talking about or what they so confidently affirm.
Human religions produce religious humans; the gospel produces godly ones. The false teachers at Ephesus represent the former; Timothy and his apostolic mentor represent the latter. The love advanced in this passage is the fulfillment of the Law (Rom 13:10). It is a summary word for the godly life. But being a law-teacher does not produce this love; for Paul, there is only one way to bring it about, “God’s redemptive plan that operates by faith” (1:4, NET). The only way to this love is divine training (BDAG) accomplished by faith.
So why must Timothy continue to work to silence the false teachers? Because their ignorant and heterodox teaching of the law works against God’s training in love by faith. To promote the program of divine training in love by faith, Timothy must silence the ignorant, heterodox, and counterproductive law-teachers. There is an inescapable link in Paul’s mind between the gospel and godliness. One cannot have the kind of love God desires without the gospel; and, therefore, if love is to be promoted, the gospel must be preserved.
This results in two questions by way of application:
Are we seeking to silence falsehood?
Are we silencing falsehood to promote God’s training in love by faith?