Re: Other than human, non of our genes can be said to be of any pure race
I hate to break it to you, but part of the definition of species is that two members of the same species can generate viable, fertile offspring.
Actually, no, this is not how species is usually defined in modern biology.
I am just too lazy to type up the definition from a textbook, so I'll copy-paste the substantially identical text from the Wikipedia article on species:
Mayr's biological species concept
Ernst Mayr proposed the widely used Biological Species Concept.
Main article: Biological Species Concept
Most modern textbooks use Ernst Mayr's definition, known as the Biological Species Concept. It is also called a reproductive or isolation concept. This defines a species as groups of actually or potentially interbreeding natural populations, which are reproductively isolated from other such groups".
It can be argued that this definition is a natural consequence of the effect of sexual reproduction on the dynamics of natural selection. Mayr's definition excludes unusual or artificial matings that result from deliberate human action, or occur only in captivity, or that involve animals capable of mating but that do not normally do so in the wild.
Many other definitions of species exist as well.
In any event, the definition of species boundary is rarely clear-cut, especially for the evolutionary closely-related organisms. In the case of the Homo genus, some authors consider Neanderthals and Denisovans to be species; others are more inclined to call them sub-species. Molecular biology evidence seems to suggest that both are sufficiently genetically distinct from modern humans to qualify as separate species.