Contradiction with Colossians 3:22
Commands servants to obey their masters in all things, whereas Philemon 1:8 suggests Paul could have commanded but chose not to.
Colossians 3:22: Servants, obey in all things [your] masters according to the flesh; not with eyeservice, as menpleasers; but in singleness of heart, fearing God:
Contradiction with 2 Corinthians 8:8
Paul states he does not speak by commandment, whereas in Philemon 1:8 he implies he could command.
2 Corinthians 8:8: I speak not by commandment, but by occasion of the forwardness of others, and to prove the sincerity of your love.
Contradiction with 1 Peter 5:3
Advises leaders not to lord over others, contradicting the tone of authority Paul implies he could use in Philemon 1:8.
1 Peter 5:3: Neither as being lords over [God's] heritage, but being ensamples to the flock. [being lords over: or, overruling]
Contradiction with Matthew 20:25-26
Jesus teaches that rulers should not exercise authority over others, contrasting with Paul's implication of his authority in Philemon 1:8.
Matthew 20:25-26: But Jesus called them [unto him], and said, Ye know that the princes of the Gentiles exercise dominion over them, and they that are great exercise authority upon them.
Paradox #1
The moral conflict in Philemon 1:8 could be seen in the tension between authority and freedom. Paul has the authority to command a specific action, but he chooses to appeal for a voluntary decision instead. This raises questions about the balance of power and the importance of free will versus obedience.