The New Atheists say many silly and ill-informed things about Christianity, but this is not one of them. They are raising a serious issue, so I thought it was worth a serious answer. I'm afraid the result will be a rather long post which for the sake of the blog format I will post in two parts (Part 2 is here). Even then I will only just scrape the surface.
Lest you think this is a dry exercise in ancient history bear in mind that human rights organisations estimate 27 million people are currently enslaved around the world and somewhere between 300 and 1,000 women are trafficked into Australia every year, mostly to work in the underground sex trade.
I'll get back to the 21st century in the second post, but firstly to Paul. The foundation for Pauline ethics is found in Romans 13:8-10.
8 Owe no one anything, except to love one another; for the one who loves another has fulfilled the law. 9 The commandments, ‘You shall not commit adultery; You shall not murder; You shall not steal; You shall not covet’; and any other commandment, are summed up in this word, ‘Love your neighbour as yourself.’ 10 Love does no wrong to a neighbour; therefore, love is the fulfilling of the law.
Paul, like Jesus, was vehemently opposed to Pharisaic legalism, which saw the Law as an immutable set of instructions which must be followed to the letter. Hence, the specific instructions in Paul's letters should not be read as laws in this sense. Instead, they need to be seen as specific attempts to guide his followers as to what love demanded in their situation. Our task is not to obey them blindly, but to use them to help us answer the same question in our own situation.
Paul's letters include seven specific references to slavery. The first is found in Galatians 3:28.
There is no longer Jew or Greek, there is no longer slave or free, there is no longer male and female; for all of you are one in Christ Jesus.
This clarifies, for readers who may have been in doubt, that the ethic of love applies equally to slaves and their masters. God makes no distinction between them. There is no excuse for treating one differently to the other.
Then there are six passages which include more detailed instructions about behaviour. First, the one that includes the offending words appears in different forms in two places, Ephesians 6:5-9 and Colossians 3:22-4:1, and also in partial form in 1 Timothy 6:1-2 and Titus 2:9-10. I will look at the version in Ephesians. The instruction about slaves and masters appears as part of a set of instructions about how people should treat one another within a Christian household - husbands and wives, parents and children, slaves and masters. The underlying context is that both slaves and masters are Christians and they are being addressed together.
The introduction to this section, in 5:21, says "Be subject to one another out of reverence for Christ." This is is a general introduction which applies to all parties in all three sets of relationships, and ties this passage back to the one in Romans. Being subject to one another is equivalent to treating one another with love. Then there is the specific instruction, first to slaves.
5 Slaves, obey your earthly masters with fear and trembling, in singleness of heart, as you obey Christ; 6 not only while being watched, and in order to please them, but as slaves of Christ, doing the will of God from the heart. 7 Render service with enthusiasm, as to the Lord and not to men and women, 8 knowing that whatever good we do, we will receive the same again from the Lord, whether we are slaves or free.
This is an incredibly difficult command, because it asks slaves to obey their masters not simply as a matter of form but from the heart, as a matter of love. Slaves are being asked to love their Christian masters. But then there is the counterpart instruction to slave owners, which needs to be read alongside the one to slaves.
9 And, masters, do the same to them. Stop threatening them, for you know that both of you have the same Master in heaven, and with him there is no partiality.
If the command to slaves was difficult, this may just be even more so. Masters are being asked not simply to be fair to their slaves, but to serve them and be subject to them. The legal relationship is turned on its head.
This is a radical departure not only from Roman practice but from previous Jewish teaching. The apocryphal book of Sirach says "Yoke and thong will bow the neck, and for a wicked slave there are racks and tortures....if he does not obey, make his fetters heavy." Paul will have none of that. Instead, he seeks to transform the relationship into one between equals. Both are to serve one another, recognising that they have the same Master in heaven and are equally accountable.
So why doesn't Paul take the logical next step, and command masters to free their slaves? I'll come back to this in Part 2, but first the other two passages. The next one is 1 Corinthians 7:21-24. Unlike the Ephesians passage, this one is addressed to individuals and it doesn't assume that all parties involved are Christian. The context is a series of instructions the overall theme of which is that people should serve God wherever they find themselves.
21 Were you a slave when called? Do not be concerned about it. Even if you can gain your freedom, make use of your present condition now more than ever. 22 For whoever was called in the Lord as a slave is a freed person belonging to the Lord, just as whoever was free when called is a slave of Christ. 23 You were bought with a price; do not become slaves of human masters.
To me this, and not the Ephesians passage, presents the greatest difficulty. Part of the problem is the ambiguity of the Greek in the second half of v21. The NRSV which I am using here sounds like it is saying slaves shouldn't accept their freedom even if it's offered to them. The NIV, in the other hand, translates it "if you can gain your freedom, do so". I am no Greek scholar but from my reading the NIV's interpretation is most widely believed to be correct, and it is certainly more consistent with the end of Verse 23 - "do not become slaves of human masters".
This is a complex message, but I would suggest Paul is saying this: Slavery does not define who you are. You are set free in Christ, even if your present situation makes that seem a distant reality. Although you are a slave, you can still serve God where you are. But at the same time, slavery is not God's ultimate design for humanity. If you can get your freedom, do so. Don't seek slavery if you are not already a slave, because you belong to Christ. Paul accepts that his followers can't always change their social situation as slaves, and are powerless to change the Roman laws, but slaves are just as much able to serve God as anyone else.
The final passage is Paul's short letter to his friend Philemon. The main purpose of this letter is to request (or rather, courteously demand) that Philemon forgive and accept back his runaway slave Onesimus, who has somehow ended up with Paul in his imprisonment. Runaway slaves in the Roman empire were subject to the harshest possible penalties, including death, torture, being worked to death in the salt mines or chained in the galleys of battleships. All this, however, was at the discretion of their owners, since legally slaves were their property. Hence, Paul is asking Philemon to exercise his prerogative and show mercy. But he is also asking a whole lot more.
15 Perhaps this is the reason he was separated from you for a while, so that you might have him back for ever, 16 no longer as a slave but as more than a slave, a beloved brother—especially to me but how much more to you, both in the flesh and in the Lord. 17 So if you consider me your partner, welcome him as you would welcome me.
This is a personal illustration of the general instruction in Ephesians. Paul has sent Onesimus back to his master, at the risk of dire punishment. But he is also instructing Philemon to transform the relationship. Not only is he to regard Onesimus as his "beloved brother", he is told to "welcome him as you would welcome me." This is a huge ask for Philemon, because Paul has politely but firmly reminded Philemon that he has the right to command him, and that Philemon owes Paul his life. In other words, like the Ephesian slave owners he is being asked to serve Onesimus, rather than merely accept his continued service with good grace.
So, this is a quick overview of what Paul says. Part 2 talks about how we should understand this message in the 21st century.