To answer the question you first need to be clear about what slavery is. If we define slavery as the ability to compel someone then almost everyone agrees that slavery is actually quite good. In our modern society parents compel children, the state compels prisoners, the state compels freemen, the state conscripts freemen to die in wars.
I’m always a bit baffled at the common response that slavery is beyond thinkable. The US government is about to compel me to buy health insurance. Where will I get the money to buy that? I’ll have to work. Thus I am in effect compelled to work and in this case for the insurance companies (surely a terrible master to have). If compulsion is inherently bad then government of any form is inherently bad. Since most people, even conservatives, think some government is necessary then some compulsion is also necessary. The problem with slavery can’t be the compulsory nature. It must be something else.
That something else could be with forms of slavery where you are born into it or forced into it. Again this is problematic because I am born into the state which compels me. And states will often raid other states for the land and the people occupying it. The US has been doing this its whole existence.
So if you are going to be against slavery it seems you’d have to be against the state. Christian teaching has always maintained that God ordained the state. It seems we can’t be against the state and similarly can’t object to slavery in principle.
The answer here is clearly no, although slavery has often taken pathological forms that do – 19th century America is a good example here.
I dont think that there was anything particularly bad about 19th century US (if that is what you meant by American) slavery. Roman slavery was certainly much more terrible. Slavery in South America and the sugar islands was more brutal (slave life expectancy was much lower than in the US). US slavery was fairly benevolent.
One distinction from ancient forms of slavery was that the master did not own the life of the slave. He owned a portion of his labor. Because of this a slave could not be killed without a justifiable cause just like any other person. In fact their are cases of slaves killing their masters and being found not guilty of any crime (due to a self defense claim) by an obviously White jury. Slaves were often better treated than the hired help. Some states had Sunday laws prohibiting working slaves on Sundays. The US military to this day can punish deserters with execution. The British Navy continued to whip disobedient sailors long after slavery ended. One reason for the portrayal of the terrors of slavery without proper context is the political purpose of justifying making war on and killing 300,000 southerners.
I would say it is not naturally evil, unless you’re implying God is a schizophrenic. He pretty much allowed it in the Old Testament. Even writers like Paul do not condemn it. It’s one of those things that is culturally unacceptable.
Not only does Paul not condemn it but he sends Philemon back to his master.
How is that different from a parent-child relationship?
There is no difference. Robert Lewis Dabney, a Presbyterian minister, famous theologian, and slavery apologist made this point. And he also made the point that once the state monopolizes the power of slavery it will try to monopolize the power of parenthood. The modern state has powers in the family unthinkable one hundred years ago. Admittedly most people think that is good. But I’d dispute that.