Neanderthals weren't hairy and stooped. That's an image manufactured by museum curators who wanted to show the public "cavemen". We have no idea whether they were hairy or not. We know that they broke their bones a lot, and that the women were as likely to have broken bones (that healed) as the men. This could mean the families hunted together. Graves of Neanderthals show that the body was carefully laid to rest, as if sleeping, and was buried with flowers. One Neanderthal skeleton was of a disabled, elderly person who obviously required a lot of care to reach old age. That means they loved one another, and didn't leave someone behind to die alone. They didn't wear crude animal skins, they had awls and could sew garments. It's possible they didn't live in caves, as a 'tent peg' has been discovered.
Almost everything you know is wrong ....
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I wake to sleep, and take my waking slow. I feel my fate in what I cannot fear. I learn by going where I have to go. ~Theodore Roethke