Actually I favour a slightly different theory.
Africa is where Humans evolved. This has two consequences.
#1) Because Humans evolved in Africa, we evolved to survive there as animals! What we think of as civilisation (City building, agriculture, technology and complex culture) are cultural adaptations that have had to be made so that Humans can survive in environments that we were not evolved to survive in!
(And a Bloody good job we have made of it too! Humans have the widest range of any species! something that was achieved in pre-historic times! Had Antarctica been accessible to pre-historic humans I have no doubt that it would have been populated too!)
"Stay_at_home" African Humans had no need to develop "civilisation" they could (and did) survive and prosper perfectly well without it right up until the 19th century!
This doesn't mean they were inferior, (Though it did mean that they easily fell victim to exploitation by technically more sophisticated "Civilised" peoples) it is that it simply wasn't something that they needed to do!
#2) We initially co-evolved with the other African Animals, therefore they were "Used" to us. Everywhere where Humans migrated to out of Africa suffered huge losses amongst the local larger animals as our ancestors found them "Easy Meat" They were not used to us and had little defence against our predation. With the large herbivores out of the way Agriculture became possible. This was much more difficult in Africa, the large African herbivores were well able to withstand Human predation and their large numbers basically made significant pre-historic agriculture in sub-Saharan Africa almost impossible. Indeed large scale farming in Africa only really took off after the introduction of firearms, and even now there are still issues with crop destruction by large hungry animals.
Not being able to engage in agriculture made significant sub-Saharan African "Civilisation" somewhat difficult to develop, even had there had been a desire or need to do so!
I really don't find any contradiction between Africa being the birthplace of Mankind and yet also being the last part of the world to develop "Civilised" societies!