Evenif the most "Paedagogi" (in the classic period) were "Servi" the translation " tutor-slaves" is weird. It does not reflect the reputation and prestige of a "Paedagogus". Private teacher, private Tutor is a much better tanslation. Also educator and pedagogue could be valid translations.
A tutor and educator, isn't the same? Tutor has an additional meaning of "guardian", it's really the private teacher, and the person assigned with the task of educating a child (or possibly siblings). Being a tutor is even more than being an educator, because the tutor is fully responsible for the education, and is the guardian (morality, knowledge...). Preceptor is close.
Actually, the paedagogi page says a slave or a freedman, so tutor is in fact more general. The fact that some were slaves is not something that needs to be emphasised. Even if they all were (appaz true of gladiators) it needs not be always mentioned. Luckily they allow typing the shorter version in through the keyboard.
Yes, mostly slaves, and some freedmen. But freedmen were former slaves.
Probably: they started as slaves in this occupation, and doing their job very well, they were offered the freedom. It would explain why most of them were slaves, and some of them freedmen.
On the contrary, the slave thing needs to be emphasized, as either slaves, or former slaves had this occupation, no freemen born freemen. Anyway, the usage has already decided, and it's not only on Duo, but paedagogus and tutor-slaves are both used in English to refer to this same thing. If historians have chosen this term, it's because the slavery was an important point here.
Another word is more neutral, and is sometimes considered as synonym, it's praeceptor. But I believe praeceptors weren't all peadagogi, when all the peadagogi were preceptors.
They were all slaves or former slaves. But it's very probable that even former slaves started their career of paedagogi being a slave. You can't remove the slavery from this concept.
Oxford Latin dictionary writes this definition:
a slave who took the children to school and had the charge of them at home. (a governor, preceptor, pedagogue)