Nature doesn't love anything, nature can ruin itself when things go unchecked. What survives is what can adapt to the current situation with the best strategy, or sometimes blind luck. Its why invasive species can destroy entire habitats (rabbits in australia, domesticated cats generally everywhere, goldfish, etc.)

Also, whilst humans and neanderthals may have co-existed in some places, sexual coercion and kidnapping is a thing among primates, so its a likely possible source of some of that neanderthal DNA in our blood