Did the Neanderthals have souls? Humans were created to have dominion over the Earth. Were Neanderthals part of this commissioning? If they did not have souls, this is early evidence of humans having sex with animals. Could God have been pleased? If animal DNA has been passed down to us from soulless Neanderthals, does this mean our flesh is irretrievably contaminated from the moment of conception? Were Neanderthals in Abraham's history? If they were, were their genes, too, in Jesus, or was an exception made for him as sinlessness was the exception made for his mother? Did the genes skip his mother?
If Neanderthals had souls, why did they become extinct? Your soul is evidence that God loves you. Otherwise, you'd be a dog or a cat, each personally loved in fact and in theology by St Francis of Assisi and therefore proved to be each personally loved by God too, but not in the same way of being loved as princes and princesses of the kingdom and natural heirs to eternal bliss. Like a homo sapiens, a Neanderthal who has a soul is also a prince or princess of the kingdom. Why aren't they sharing dominion over the earth with the human species of today?
All things that could be considered while flossing and checking your gums in the mirror ....