The Qur'an Never Prohibited Slavery
I know this is going to sound cringe, but Qur'an isn't at odds with slavery and the people who claim otherwise are shooting themselves in the foot. If the Qur'an opposed slavery as an institution, it would've criminalized or prohibited it, but overall the Qur'an seem indifferent.
People complain that Islam overlooked slavery, that Muhammad or some other respected historical figures owned slaves or supported slavery, and should therefore be condemned today.
These people people don't realize that slavery continues today in form of 9 - 5 or corporate jobs that we all benefit from, support and even partake in.
Why 9 - 5 Work is Modern Slavery
Their complaint is that slaves were for forced to work against their will. Ironically, 9 - 5 workers work against their will, most of them barely endure their jobs, every morning they can't wait to return home and every Monday they can't wait for weekend.
You can say, "9 - 5 workers voluntarily applied for their jobs aware of the difficulties it entails." But realize that there were slaves that voluntarily gave up their freedom to serve a master, for reasons like abject poverty.
But 9 - 5 workers get paid while slaves get nothing, right? Wrong. Slaves customarily get housed and fed in exchange for their labor, which is why people would offer themselves as slaves to wealthy masters. In fact, some slaves lived in better condition than poor non-slaves.
If your complain is that that some slaves were poorly housed or fed, then consider that some 9 - 5 workers today barely earn enough to get by. Which is why we constantly talk about minimum wage.
Still, you may argue that 9 - 5 workers are free to quit at any time while slaves can't. Again, false. 9 - 5 workers can't just quit if they feel oppressed at work. Jobs are scarce, the fear of unemployment and going broke would more than likely force them to continue with their job. I know workers who haven't received salary for 6 months! Even they are afraid to quit their job.
Why the Qur'an Never Abolished Slavery
I do not intend to trivialize slavery. Yeah, it is worse than 9 - 5 work. But it's closest approximation today is 9 - 5 work. And just as today people look back at slavery as a very horrible thing, people in a few centuries will look back at 9 - 5 work as a very terrible state.
Yet as bad as 9 - 5 work is, our society can't do away with it. It is impossible for every one to be self employed. And even if it were possible, quality of services would drop and price would either soar or plummet.
In the end, the reason the Qur'an seem indifferent to slavery is clear. Abolishing it in absolute term is just impossible. Every society depends upon some variation of slavery to sustain itself. At best we can improve the condition of slavery but abolishing it entirely is unlikely.
Peace.