To Philemon our beloved brother and fellow worker... and to the church in your house: Grace to you and peace from God our Father and the Lord Jesus Christ.
Phil. 1-3 ~~ Paul's letter to Philemon was written at the same time as his letter to church at Colossae, and was delivered to Colossae by the same messengers: Tychicus and Onesimus (Colossians 4:7-9).
Phil. 4-10 ~~ Paul does not immediately mention the purpose of the letter, but tries to build rapport as a pastoral and apostolic authority over Philemon as a believer.
Phil. 4-5 ~~ Paul's spirit of thanksgiving arises out of Philemon's love "toward the Lord Jesus and toward all the saints."
Phil. 6 ~~ Fellowship of Christian faith becomes "effective through the knowledge of every good thing which is in in you for Christ's sake." Fellowship and Christian community is reinforced and made complete not only by recognition of the value of others, but also by the recognition of the value of oneself ("every good thing which is in you")!
Phil. 8-9 ~~ Paul clearly states that he has "enough confidence in Christ" (i.e., enough moral confidence in his beliefs) to demand and order a certain course of action, "yet for love's sake I rather appeal to you." Paul returns to this theme in verses 14 and 21, speaking of his desire that Philemon will obey freely without coercion from a spiritual authority. Paul restates in verse 19 his authority to demand obedience ("you owe to me even your own soul as well").
Phil. 10 ~~ Paul finally comes to the point of this personal letter: "I appeal to you for my child Onesimus." This direct appeal comes only after Paul had build up his own credibility (ethos), and is followed by passages that demonstrate the logic of his request (logos) and that reach out to Philemon's conscience and heart (pathos). Paul was a well-educated Pharisee, who was familiar with the Hellenistic culture. The epistle to Philemon is a clear instance of classical rhetoric as developed by Plato and Aristotle.
Phil. 11 ~~ Paul makes a lighthearted pun on the meaning of Onesimus' name ("useful"). Wordplay was a common feature in classical rhetoric.
Phil. 12-14 ~~ Paul's reasons for sending Onesimus back: "without your consent I did not want to do anything, so that your goodness would not be, in effect, by compulsion but of your own free will." This sounds noble, but is incredibly problematic. Paul is delivering Onesimus, a runaway slave, to the estate of his master Philemon, to face probable execution under Roman law. In sending a fellow Christian to the very teeth of persecution without security and only hope. Paul doesn't even exercise what leverage he has to ensure the safety of Onesimus. Paul expresses only his love for Philemon as reasons for his actions, but if that were the sole consideration for his actions, Paul would have failed to act lovingly towards Onesimus. Onesimus must have been consulted, and must have agreed to return to Philemon; otherwise, Paul's actions are indefensible.
Phil. 15 ~~ Paul contrasts the temporary deprivation of a servant with the eternal gain of a brother. "Perhaps he was for this reason separated from you for a while, that you would have him back forward."
Phil. 16 ~~ Paul requests that Onesimus be accepted back and his offenses forgiven, and that Philemon treat this runaway with all of the consideration and love he would regularly extend to his fellow believers. Paul does not directly request Onesimus' freedom, but only his forgiveness ("no longer as a slave, but more than a slave, a beloved brother.") As with similar passages in Ephesians and other NT epistles, Paul's emphasis is to redeem rather than replace social institutions. Paul addressed the individuals within the system and give them guidance to acting with virtue.
Phil. 17-21 ~~ Paul makes an emotional appeal to Philemon, appealing to feelings of gratitude, honor, and even Philemon's sense of pride.
Phil. 19 ~~ Paul restates his ability to command and demand obedience ("you owe to me even your own self") but appeals not to Philemon's humility but to his gratitude and to his trust ("I will repay it").
Phil. 20-21 ~~ Paul appeals to Philemon's sense of pride, not only in being in a position to "refresh [Paul's] heart in Christ," but also in being entrusted with Paul's confidence that he would exceed every expectation on his virtue. Sins and errors are dangerous in proportion to the value and impact of the virtue or truth they distort. Humans struggle with pride so often because the underlying virtue is so foundational: we were created in the image of God, and shall be raised to glory with Christ.
The grace of the Lord Jesus Christ be with your spirit.