"Slaves, obey your earthly masters with respect and fear."
"Slaves, in reverent fear of God submit yourselves to your masters, not only to those who are good and considerate, but also to those who are harsh."
"Teach slaves to be subject to their masters in everything, to try to please them, not to talk back to them,"
Bring this up to any Christian in a debate and all you will hear is denial, denial, denial. They will say things like, "Biblical slavery wasn't really slavery, it was voluntary servitude." This is an outright lie that has been debunked so many times it's not even funny. Just check out for example Thom Stark's critique of Paul Copan's attempt to justify this response here in his two chapters on biblical slavery in Is God A Moral Compromiser?
Christians might also try to use Colossians 4:1 which says "Masters, provide your slaves with what is right and fair, because you know that you also have a Master in heaven." They'll use this passage to say that god wanted masters to treat their slaves decent and with respect, and that slavery "back then" was different. But the Christian would of course be forgetting that 1 Peter 2:18, which I quoted above, says slaves are to obey ALL masters, both the kind and the cruel. And of course, the central objection to the New Testament is overlooked in this response—that is the issue of slavery itself. Who cares if the master is nice. The master is still owning another human being as property, and god is perfectly fine with it.
Another objection Christians will use to object to slavery is a passage in 1 Timothy 1:10, which is supposed to condemn "the sexually immoral, those practicing homosexuality, slave traders and liars and perjurers—and for whatever else is contrary to the sound doctrine."
There are at least three ways you can react to this passage in 1 Timothy. First, it still makes it OK to purchase slaves from others who may have kidnapped other people into slavery, or who have sold their daughters into slavery, or who are selling slaves they have inherited as property (which Leviticus 25:44-46 allows). 1 Timothy 6:1-2 even says that good obedient slaves glorify god by serving their masters well. So this passage doesn't condemn the institution of slavery, just one aspect of it.
Second, if this passage in 1 Timothy is granted, then the Christian will have to also grant other passages in Timothy, such as 2:12 which says "A woman [or wife] should learn in quietness and full submission. I do not permit a woman to teach or to assume authority over a man; she must be quiet." This means that if kidnappers are wrong, then so are assertive women who forget their place in society and marriage, which is in full submission to men.
Earlier in the chapter it also instructs that good Christian "women [are] to dress modestly, with decency and propriety, adorning themselves, not with elaborate hairstyles or gold or pearls or expensive clothes." There goes half the economy.
Thirdly, and perhaps most damning to this passage in 1 Timothy is that nether 1 Timothy nor 2 Timothy are considering authentic letters from Paul by many scholars. New Testament scholar Bart Ehrman writes in his book Lost Christianities: The Battles for Scripture and the Faiths We Never Knew, "The pastoral epistles of 1 and 2 Timothy and Titus: They claim to be written by Paul, but appear to have been written long after his death." (p. 11) And he notes that "most critical scholars think that 1 Timothy is pseudonymous: its vocabulary, writing style, theological modes of expression, and presupposed historical situation all differ significantly from what can be found in Paul's authentic letters." (p. 38)
Erhman also notes in Forgery and Counter-forgery: The Use of Literary Deceit in Early Christian Polemics on 1 Timothy:
There are numerous other points that stand in tension with the historical Paul...Spiritual charisma is received by laying on the hands rather than baptism (4:14); God is the savior "especially" to those who have faith (especially? 4:10); widows are to be enrolled in the church, showing that the church is becoming a social institution (5:9); the presbyteroi—a word and concept found nowhere in Paul—are rulers of the church who deserve to be paid (5:17-18); the written words of Jesus are now scripture (1 Tim. 5:18; cf 1 Tim. 6:3); and on and on. Again, a few of these comments—and there are many more like them—may be explained away in isolation as a sensible development from Paul. But it is the collocation of odd comments, in combination with so many other factors, that shows that this is a book written after Paul's demise, by someone living in a later context when the church is established and settling in for the long run. (p 208)
Of course an evangelical Christian will contest the idea that any books of the Bible are inauthentic, and most likely no evidence you can show them will change their mind. At best, you will be able to do is plant a seed of doubt in them, and hope it grows into a tree of skepticism. But if a Christian objects to the accusation that the New Testament condones slavery by citing 1 Timothy 1:10, you will know this verse's very authenticity is in dispute by a large numbers of scholars.