It's actually not, whether you're talking about individual freeing of slaves (which has basically been a thing since slavery was instituted at all) or nation-scale emancipations.
A careful reading of that timeline and its sources shows that all the "emancipations" listed before the 18th century are highly localized and/or short-lived, so I would agree that the widespread concept of freedom from slavery as an inalienable right is fairly modern.
So if freedom from slavery. So?
Besides, democracy was formally conceptualized 2.4 millenia ago, in ancient Athens. And it was practiced even before in various forms.