The main purpose of the letter is to instruct Timothy about refuting false teachers. Paul does not give an exact description of these false teachings, but they seem to be along the lines of what would become known as “Gnostic” teachings: physical things are evil so Jesus cannot have come in the flesh, certain people possess critical secret knowledge that leads to salvation, and secret ways to have access to an unknowable God.
Paul opens his letter by reaffirming his own credentials and restating the true Gospel. Since Timothy had been Paul’s close companion for more than ten years, he certainly had heard all these things before and was totally convinced of their truth.
In the second chapter, Paul addresses matters having to do with orderly and proper worship that will lead to unity of the church, as the church in Ephesus had to blend people from various cultures, ethnic groups, economic circumstances, and social classes. Imagine an older, male Jewish goldsmith well-versed in the Old Testament worshiping alongside a young female slave who had previously worshiped at the temple of Artemis.
With those thoughts in mind, recognize that the third chapter is Paul’s instructions about appointing a new kind of leader. Roman leadership was dominated by rich people and government officials. The church was going to need a new type of leader, and it would have to cultivate, grow, and teach them to become the type of people they needed to be.
All of those thoughts lead to the rest of Paul’s teaching on growing and unifying a church. Through all his instructions, Paul’s love and concern for Timothy shine through.