It may have been the WEATHER that did them in. Researcher Julien Riel-Salvatore says, "It’s been long believed that Neanderthals were outcompeted by fitter modern humans and they could not adapt. We are changing the main narrative. Neanderthals were just as adaptable and in many ways, simply victims of their own success."
Researcher Michael Barton agrees and says, "Neanderthals could have disappeared NOT because they were somehow less fit than all other hominins who existed during the last glaciation, but because they were as behaviorally sophisticated as modern humans."
The last Ice Age saw hunter-gathers, including both Neanderthals and the ancestors of modern humans, range more widely across Eurasia searching for food over a period of 100,000 years, during a major shift in the Earth’s climate, leading to culturally and environmentally driven changes in land-use behaviors of both early humans species.
Since neither species stayed in one place as they roamed the world for food, they interacted–and interbred–more often, leading to the demise of the Neanderthals. Riel-Salvatore says, "Neanderthals had proven that they could roll with the punches and when they met the more numerous modern humans, they adapted again, but modern humans probably saw the Neanderthals as possible mates. As a result, over time, the Neanderthals died out as a physically recognizable population."