I thought that there were sizable modern populations with no Neanderthal DNA which would suggest that they are not ancestors of modern humans:
https://en.wikipedia.org/wiki/Archaic_human_admixture_with_m...
https://en.wikipedia.org/wiki/Archaic_human_admixture_with_m...
Various sources of Archaic admixture have been observed or postulated for different modern human groups; determinations about their similarity to modern humans are made in broader grounds. As a practical matter, taxonomic distinctions between different hominid species/subspecies are generally retained until sufficient evidence accumulates to justify dissolving the boundaries. The idea that archaic groups like Neanderthals were very cognitively sophisticated has been around for a long time; the question is whether it is more informative to maintain them as different taxa.