St. Paul lived in a world where there were slaves. The economy of the ‘ancient world’ depended on slave labour, as did our own until the industrial revolution, when it shifted from out-and-out slave labour to the factory floor.
Paul’s injunction that slaves should obey their masters seems to me less a ‘let there be slavery’ statement, and more a realistic assessment of the opportunities for spiritual growth that any status quo presents. Your master had the right to beat you, to sell you, and if you engaged in revolt, you could be crucified. He recognized that placing oneself in service to another human is always a strong spiritual path, and he reminds the slave that he is, after all, serving God when he serves any other human being.
I find it useful to read the ‘wives, submit to your husbands’ directive in the same context. Women at that time were chattels. Not submitting wasn’t really an option, but submitting to the man of the house as a surrogate for God made an interesting choice. Paul was by no means a social revolutionary, and it seems likely that a major concern for him would be rendering Christianity as acceptable to the largest number of people.
He does, of course, include instructions for husbands, and for the owners fo slaves. They must remember that the people who serve them, serve God, and that to abuse or mistreat any servant of God is wrong. This is true, and good, and perhaps the furthest one can go. A master has the choice to abuse his slave; the slave cannot choose to disobey. Ditto wives.
I don’t think any of this invalidates Paul’s wisdom or his inspiration. I think it shows rather that he was working consciously and compassionately within a social order he chose not to attack. Jesus can be seen as a revolutionary; Paul cannot.