but even in ancient Greece and Rome there existed some legal protections for slaves

We don't know much about Greece, but in Rome if you were released from slavery (by the master's will, contract expiring, etc.) you were treated equally to people that haven't been enslaved at all. And slavery was extremely common, independent of your state allegiance or color of skin.

That being said, we're talking about a deeply fucked up system where the paterfamilias held complete control over not only his slaves but his wife, children, the entire family. And being treated "equally" to other commoners in Rome isn't really saying that you were treated any good.

The main difference is that slavery as in the USA went through so many iterations of bad faith laundering that it had an entire ideology tacked on top to explain why it was good and Christian, actually. In Rome no one bothered, it was a clear power dynamic - we conquered you, now we own you because we have bigger dicks, simple as that.