Reality doesn’ t always conform to the nice neat boxes that people want to segregate them into, but even the most extreme lumper taxonomist doesn’t classify wolves and coyotes as the same species. Inability to easily reproduce together is a possible effect of a long reproductive separation. It is not what defines species.
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 ;-)