True, some of the left-right spectrum was a mixed bag of contradicting ideas.
In antiquity, slavery was conceived of as a part of 'property rights', whereas later philosophers like John Locke changed our understanding of slavery and concluded that we cannot own other people as property.
Classical slavery was from the Lockean perspective the anti-thesis of property rights and the primacy of every individual to be sovereign and own themselves.
If the individual can't own themselves, then property rights doesn't exist. Hence slavery undermines the basis of property rights; every individual owning the fruits of our labor.
A slave is not allowed to own the fruits of their labor, because they are not recognized as the sovereign masters of their own mind and body.