jp1692 - "Neanderthals have contributed approximately 1-4% of the genomes of non-African modern humans, although a modern human who lived about 40,000 years ago has been found to have between 6-9% Neanderthal DNA (Fu et al 2015). The evidence we have of Neanderthal-modern human interbreeding sheds light on the expansion of modern humans out of Africa." - (Click the link above to read the full article)
I am fully aware of that. The problem is that you have no idea what you're reading.
Again, Homo sapiens did not evolve from Homo neanderthalensis. Homo sapiens evolved from Homo heidelbergensis. Once our species appeared and moved out of Africa, our ancestors started interbreeding with the neanderthals. All that means is that modern non-African humans have neanderthal DNA (they are descendants of the neanderthals.) As a species, however, we did not evolve from them. They are our cousins. Richard Dawkins said as much in his conversation with George Pell, but when he was explaining it, he was interrupted. Hence, he didn't get to explain it, but he did say that Homo neanderthalensis are not our ancestors (as a species):
https://www.youtube.com/watch?v=sZobzGgE5KE
If you don't trust me on this, trust an expert.