At first glance, this seems to be the perfect opportunity for Paul to denounce the practice of slavery. By most accounts, Philemon was intended primarily as a personal letter from Paul to Philemon asking him to receive his runaway slave back. Why wouldn't Paul use this opportunity to ask Philemon to stop keeping slaves or at least to release Onesimus? I think that the answer to that question leads us to and resides in the heart of the gospel.
The bible is very clear that in Christ, God makes no distinction between slave or free man in terms of the worth of a person (Galatians 3:28, Colossians 3:11). Yet Paul never teaches, encourages, commands anyone to free slaves nor does he encourage slaves to escape from their masters. Paul gives instruction to slave masters on how to treat slaves (Colossians 4:1, Ephesians 6:9) and he instructs slaves to obey their earthly masters (Ephesians 6:5-8, Titus 2:9-10). The patterns here is that instead of speaking to the institution of slavery, Paul speaks to the participators in the institution. In his letter to Philemon, again Paul's focus in on the people involved, in this case Philemon and Onesimus, rather than the institution of slavery. Is Paul skirting the issue of slavery? Is he condoning it? What is Paul's reasoning behind his method of addressing this issue?
Paul's concerns in the letters he writes in the New Testament seem to be primarily two fold: first, that the churches and people he writes to believe, teach, and preach the one true gospel and second, that individuals conduct themselves in a manner consistent with a belief in the one true gospel. Paul knows that the gospel is the only means by which a man or woman can be saved from sin. This message is more important to him than any other. This gospel is so important that in his letter to the Galatian church, Paul says that if anyone teaches a false gospel, he is to be accursed(Galatians 1:8-9). Nothing is more important to Paul than Jesus Christ and His gospel. Paul is much more concerned with dealing with issues of the heart than he is social or political institutions. Paul writes to ensure that the gospel is understood by, taught by, and has tranformed the heart of the readers.
A look at the ministry of Jesus reveals the same concerns. Many of the Jews of the day expected that Jesus, as Messiah, had come to overthrow the oppressive Roman government and re-establish a Jewish kingdom on Earth. Jesus made it clear that He had no interest in such things (John 18:36). He even told the Jews to continue paying taxes to the very same oppressive government He was asked to overthrow (Matthew 22:21). His purpose was to do the will of His Father by becoming the perfect substitution for His people on the cross, conquering death by His resurrection, and returning to the Father to mediate on our behalf. Jesus, like Paul after Him, was much more concerned with the hearts of men than He was their institutions (including their religious institutions at times).
Specifically in Philemon we can see Paul's concern with how the gospel tranforms the heart. Paul states that he had the apostolic authority to command Philemon concerning Onesimus but that he preferred not to. Rather, he chose to appeal to Philemon to do what was right concerning his runaway slave (Philemon 8-9). Paul was convinced that because of the transforming power of the gospel in Philemon's life he would choose what was right (Philemon 21).
The gospel is not about overthrowing evil or immoral institutions but about reconciling individuals back to the God who created them. Social and political change, if it is to happen, will occur from the inside out and one person at a time. Our calling is to be ministers of reconciliation (2 Corinthians 5:18) to a world of people who desperately need the good news of the cross.