The real worry is that the Bible does not say anywhere NT or OT not to have slaves. As previously mentioned there are countless texts in the NT where Jesus, Paul etc are telling slaves to be obedient, but not once does it say slavery is evil. So much for moral superiority.
Jesus was not a reformer, neither was he a philosopher. The time we spend on Earth is fleeting and whether we live in servitude or not is of secondary interest to God as far as our individual lives are concerned. But Christianity was anti-slavery in that it emphasized the freedom and agency of all men to be obedient to God. What is important is our moral outlooks, our keeping the commandments. This is not to say that slavery isn't evil. It is. Very much so. But Christianity had little to say on it because its message was Christ, and the freedom Christ offered was of far greater worth than any other types of freedom. Jesus also wasn't a lawgiver like Moses was.
Christians weren't permitted to own slaves, and under the Law of Moses, servitude was limited to restoration. You couldn't just declare bankruptcy if you owed a debt you couldn't pay, neither were there debtor prisons. And servitude wasn't forever under the Law. Every seven years or so, you had to forgive all debts. Slavery in the U.S. (and it wasn't just in the South; the Emancipation Proclamation didn't free one slave anywhere, and it didn't apply to slaves in the North). Under the Law, you couldn't beat a man to death. Once you drew blood, you had to stop. Not so in Europe and the U.S.
Jesus' message was one of hope and freedom. It had to do with the redemption of mankind from the fall. In the Second Century A.D., as Christianity began to spread, converts freed slaves right and left. That's because it changes the heart, or it's supposed to.