myths and endless genealogies … speculation: Paul might be dismissing their teachings as not significant, or he might rejecting their interpretations and their justification of bad behavior (1:7; see also 2 Timothy 4:3–4; Titus 1:14; 3:9; 2 Peter 1:16; 1 Timothy 1:8–11; 4:1–2, 7; see also Titus 1:15–16).
endless genealogies: In Judaism, a genealogy (list of ancestors) established a person's spiritual heritage. The false teachers might have focused too much on this. They probably also used Old Testament genealogies in imaginary interpretations of the law (Genesis 2–4; 5:1–32).
rather than the stewardship of God’s work, which is by faith: The Greek uses an important word (“stewardship,” “household management”) connected to managing a household (see 1 Timothy 3:15). This phrase can also imply other meanings, including faithfulness to God's household management or faithfulness in managing God's household.