CLAIM: Paul writes, “I appeal to you for my child Onesimus, whom I have begotten in my imprisonment” (Phile. 10).
RESPONSE: Obviously not! This would mean that Paul had a conjugal visit while in prison (“begotten in my imprisonment”), and Roman prisons didn’t have these privileges. This interpretation would also mean that Paul sent a toddler back to Philemon (!!). Instead, Paul refers to people he’s led to Christ as his children (c.f. 1 Cor. 4:14, 17). N.T. Wright explains, “The Rabbis used the metaphor of sonship to describe the teacher-pupil relationship: Paul was fond of using it for that between himself and his converts (1 Cor. 4:14–15; 2 Cor. 6:13; Gal. 4:19; Phil. 2:22; cf. 1 Tim. 1:2, etc.).”
 Wright, N. T. (1986). Colossians and Philemon: an introduction and commentary (Vol. 12, p. 188). Downers Grove, IL: InterVarsity Press.