The Neanderthaler in me

Recently the news hit the headlines that Neanderthals had some DNA of Homo sapiens in their genome. Before that, the reverse had already been demonstrated, namely that modern people can have Neanderthal genes. And because not all individuals have the same Neanderthal genes, if you add all those genes up, the complete human population has a considerable amount of genes that once made a Neanderthal tick.

That modern people have genes in their genome that can be traced back to our Neanderthal cousins is only true for non-African populations. The mixing between the two Homo species probably happened in Eurasia, when H. sapiens populated areas already inhabited by Neanderthals. The latter never lived in Africa, which is why genuine African populations don't have any Neanderthal DNA in their genome.

Now the scientific literature starts to report effects of this 'foreign' DNA in our genome. A frequently expressed expectation is that there must be negative effects. But why? Neanderthals branched off from H. sapiens relatively recent, so in a way their DNA used to be that of our own ancestors, in a more distant past. A more positive view would predict that Neanderthal genes can be good for us.
One thing that these discoveries haven't solved for sure is whether H. sapiens and H. neanderthalensis were separate species. That babies were produced from their encounters, and that these babies were fertile, suggests that the two are only subspecies. (The production of fertile offspring is one of the main criteria for defining species). But the story is more complicated than that. It seems that of the hybrid children, only the females reproduced. This may suggest that the hybrid boys were infertile, a hint that the two populations had been separated long enough to indeed evolve into separate species.
Or it may suggest that the hybrid men were not liked by women, at least not by Homo sapiens women. Somehow, I can sympathize with that idea.