>The concept of species seems vague and not very scientific.

That's because applying any sort of strict categorization to a very fuzzy system isn't going to go nicely. Animals don't just gain a feature and are suddenly unable to reproduce with similar creatures, inability of interbreeding is based off of what specific mutations any individual species has gained. You can have extremely different organisms that are capable of interbreeding or you can have extremely similar organisms that are incapable of interbreeding. You can even have a set of ring species where species A can breed with species B, B can breed with C, C with D, D with A, but A cannot interbreed with C, nor can B breed with D.

Capability of interbreeding seems like a nice clean dividing line for species, but nature doesn't divide things up nicely into boxes. A taxonomy based off of genetic drift with speciation based off of morphology and behavior is the best we can do to satisfy the human need to categorize everything into nice compartments. If a neanderthal has a different set of bones and body structure as well as a radically different primary diet and metabolism, why does it make sense to talk about it as the same as Homo Sapiens?