IMHO, poor old Mr. N. has had a rabidly bad press over the decades.
"Microcephalic idiots" Their average brain size was larger than ours.
"Neanderthals couldn't do more than grunt". Their delicate hyoid bone, just like ours, "speaks" against us. It's a considerable disadvantage to humans, meaning we can be choked by a sharp tap to the throat. It would need a HUGE compensating advantage for that not to be evolutionarily edited out. In humans, that advantage is the facilitation of complex spoken language. Now, what could it be in the case of Neanderthals ...?
"They shambled along with their knuckles scraping the ground." The first specimen found had absolutely crippling arthritis in the hips. Hardly a representative sample.
"They had no consciousness about the world outside themselves." What about all the carefully laid-out burials with different types of flower pollen? "They fell into pits and were buried by animal activity. The flowers must have just fallen in, too." What sorts of flowers grow in dark caves?
Hey, guys: They made fire. They wore clothes. They made tools. They religiously buried their dead. They CERTAINLY talked.
The only creatures who do that today are PEOPLE! Yes, Neanderthals were apes - physiologically, so are modern humans. Yes, they were animals - but lofty Homo sapiens sapiens is within Kingdom Animalia, too.
Neanderthals were people. They were around before us, and they lived alongside us for tens of millennia. They survived freezing Ice Ages and hot Interglacials. Why not honour them as a successful cousin rather than as a botched attempt at humanity?
A shambling, moronic creature like the stereotypical Neanderthal wouldn't last five minutes in Darwin's rough playground, let alone 320,000 years.
When H. sapiens sapiens has lasted that long, perhaps we can mock him with greater authority.
Welcome, Neanderthal. Even if you're not my direct ancestor, I hail you as a cousin.