Preface: After I wrote this response I found an article that articulates what I said and more much better than I have, but I'll leave what I wrote any how. Here is the article:
Does the Old Testament condone slavery? | GodWords: Theology and Other Good Stuff
In Leviticus:
39 “If your brother becomes poor beside you and sells himself to you, you shall not make him serve as a slave:40 he shall be with you as a hired worker and as a sojourner. He shall serve with you until the year of the jubilee.41 Then he shall go out from you, he and his children with him, and go back to his own clan and return to the possession of his fathers.
In Exodus:
"When you buy a Hebrew slave,[a] he shall serve six years, and in the seventh he shall go out free, for nothing.3 If he comes in single, he shall go out single; if he comes in married, then his wife shall go out with him."
So the Israelites are not to be treated as the foreign slaves are treated. But even the foreign slaves are not treated poorly,
"If a slave has taken refuge with you, do not hand them over to their master. Let them live among you wherever they like and in whatever town they choose. Do not oppress them." - Deuteronomy 23:15-16
He then goes on to say how bad slavery was, by quoting Exodus 21:7-11, which says that if a master marries his slave he must treat her as a wife, and if he fails to do so, he must set her free.
Then he says that if a master kills a slave, the master should be killed, but if the master beats the slave, and days later he dies (this would be an accidentally death), the master is not to be killed.
One thing that he does a lot that is not logically supportable is to take the implicit prepositions God is making, such as, "If you marry your slave then you must treat her as a wife" and conclude from this that God is condoning the antecedent, that is, in this case, that marrying your slave is good, and as he goes onto say, that marrying multiple women is good. We know this is not the case, because he says things like, "If you kill your slave then you shall die", and we know that God does not condone killing your slave. Likewise, from Exodus, the verse,
Exodus 22:1616 "If a man ENTICES a virgin who is NOT BETROTHED (engaged), and lies with her, he shall surely PAY the bride-price for her to be his wife.
Contains the proposition that is essentially, "
If a man commits consensual fornication with a women,
then the two shall become married." That doesn't mean that fornication is good. Another example that makes the point even clearer is when God says that
if a man rapes a women, who is not engaged to a man,
then he must support her for the rest of his life, because he has essentially ruined her chances of marrying another man by raping her. God isn't condoning rape just because he is anticipating it. Just because God says that someone should not be put to death for something, doesn't mean he is condoning it.
So after he makes a whole bunch of assumptions about God's character that are not justified, he goes onto again misunderstand the difference that is to be made between Hebrew slaves and foreign slaves.
After this he talks about slavery in the new testament, but he doesn't really say anything important there, other than, "Look it's still a thing here!"
Also, remember that he has hand picked the verses carefully to try to make the whole slavery process look ruthless, and even these verses are not as bad as he is making them seem.