Given time and effort, one could THEORETICALLY start with a pair of wolves and produce “Beagles” but the reverse is not true, as the genes for Wolf morphology have been bred out of the Beagle population.
Definition of “species” via the discipline of taxonomy was not my point. My original point is that Neanderthals were Homo sapiens genetically, and could readily inter-breed with Homo sapiens sapiens today ... given enough money.
My point comes from a genetics perspective: we and Neanderthals share the same genes/chromosome pairs. (unlike chimps and humans for example). Our gametes are compatible, if not our morphology ;-)
Given enough time and effort one could get a wolf like dog from a beagle. None of the changes in DNA are irreversible. And Neanderthal were Homo Neanderthal not Homo Sapien. They were a distinct and separate population.