The commentary on the Gospel reading can be found here. The NT reading is
Paul appeals to Philemon on a number of grounds, Chrysostom tells us in his Homilies on Philemon: the quality of his person, his age, and most of all, because he is a ‘prisoner of Jesus’. Paul speaks eloquently of Onesimus, in exactly the same terms he uses for Timothy, and he reminds Philemon that his slave is born again in Christ. Paul is mindful that Onesimus still belongs to Philemon, and so he brings before him the admirable qualities which he says will be useful to him (Paul) in the service of Jesus. God rules, Paul reminds him, not by tyranny or coercion, but by love and encouragement – he wants us to willingly give ourselves to his service – and this is the model which Paul suggests to Philemon with regard to Onesimus. Since it would be to the glory and service of God, Paul suggests that in behaving as God wants, Philemon would be doing a good work in helping Onesimus to help Paul spread God’s word.
St Jerome thought that verse 14. in which Paul talks about goodness not being by compulsion, answers the question of why God gave man free will and did not just make us automatically good and obedient. God is good not by some impersonal necessity he is so, but because it is in his essence that he freely wills his own goodness, and since we are made in his image, he wants us to choose to be good.
Paul wisely uses the word ‘perhaps’ in verse 15, since Onesimus did not flee his master to achieve God’s work, but from the desire to escape his master; this is also designed to show Philemon that Paul is judging impartially.
Chrysostom comments on the uselessness of names in describing good and evil in men, for there are many who are masters who are wicked, drunkards and dissemblers, and many a slave who is upright and good. Is the man who is slave to drink or greed in any way really free? Sin is the harshest of slave masters. Paul shows Philemon how wonderful God’s ways are and invited him to cooperate in the spreading of the Good News.