If you are going to be ludicrous leave the debate. Humans and sperm whales have never shared hunting grounds :)
Your wrong visibly deformed children are not always killed in Hunter Gatherer cultures especially those cultures in very rich environments such as Western Europe. You are getting your evidence of this practice from African H&Gs living in very marginal environments.
Also how do you know what Neanderthal societies did with deformed children? I mean you are the one that keeps saying they were so strange we can't even understand them.
However I can show ample evidence that cripples and the deformed were cared for in cultures at the time from the fossil record. Hell Neanderthals were known for caring for their crippled and deformed members.
For our purposes it doesn't matter what Neanderthal societies did with deformed children. 100% of Neanderthal societies are extinct, along with any hybrids that might have remained in them.