How can anyone get DNA results not showing some African DNA if we all came out of Africa?

How is it possible for some Europeans to have an ancestry DNA test done and not show some amount of African DNA if we all came out of Africa? Even the Chinese have discovered recently, to their surprise, that their ancestry is linked to Africa. What is going on here? In order to completely breed out the African DNA, you would need some DNA that was uniquely different from African DNA...Wouldn't you? That would seem to imply that when African Humans migrated into Europe and mixed with Neanderthal, the Neanderthals did not go extinct, but are rather alive and well. Can someone explain this? In order for the African DNA to be completely eradicated from the European DNA, there would have to be some other type of DNA other than African for that to happen. Otherwise the African DNA should still be present in Europeans. What's going on here?