From a Puritan Board discussion on why the Apostle Paul didn’t command Philemon to immediately release Onesimus as a slave:
Bill the Baptist (Comment 2):
People have often criticized Paul for not explicitly insisting on the release of Onesimus, but if you read carefully, you will see that what Paul suggests is far more radical. Paul asks Philemon to receive Onesimus as a true brother in Christ, which if he were to actually do, would very naturally make it impossible to continue to enslave him. Paul understands that the hearts of men cannot be changed by law, but only through the gospel.
Alan D. Strange (Comment 3):
While it is true that Christ and the apostles did not abolish slavery, it is also the case that the consequences of the gospel would tend to ameliorate if not eliminate such (seen in Paul’s letter to Philemon).
Had Christ or Paul ordered the end of all slavery, it would have rendered the gospel revolutionary and made its central concern social, political and economic equity. If Paul, for instance, had simply commanded Philemon to free Onesimus and not suggested that he be emancipated as a consequence of the new relationship that they sustained in the gospel, Christians would have viewed such an apostolic command as binding, necessitating the abolition of slavery immediately everywhere. This would have obscured the true spiritual message of the gospel—salvation in Christ to all that believe on Him—and have rendered the Christian faith another competing, indeed radical political agenda, especially in the Greco-Roman world, with so much of the population in slavery. The New Testament contains no explicit commands to abolish slavery—though it prohibits man-stealing (I Timothy 1:10) and thus proscribes American slavery—leaving it to the outworking of the gospel to address such in the Greco-Roman world of its day.
 As seen in the practices of Christians in the early church, in A. J. Harrill The Manumission of Slaves in Early Christianity. (Tubingen: J. C. B. Mohr/Siebeck, 1995). Though opposition to slavery itself, as opposed merely to slavery’s abuses, was long in coming, as seen in Trevor Dennis, “Man Beyond Price: Gregory of Nyssa and Slavery,” in Heaven and Earth: Essex Essays in Theology and Ethics, ed. Andrew Linzey and Peter J. Wexler (Worthing, West Sussex: Churchman Publishing Limited, 1986), it was Christianity, or Christendom, at least in part, that brought slavery to an effective end between the fourth and tenth centuries, with serfdom developing in seignorialism and feudalism subsequent to slavery’s diminution.
 Though Kyle Harper, in Slavery in the Late Roman World, AD 275-425 (New York: Cambridge University Press, 2011), showed that slavery lasted deep into the Christian era, in his most recent book, From Shame to Sin: The Christian Transformation of Sexual Morality in Late Antiquity (Cambridge, Mass.: Harvard University Press, 2013), he shows that Christianity’s strict moral code was particularly sympathetic to the sexual exploitation of the slave. So Christianity played an important role in reforming and ultimately ending ancient slavery.