I'm afraid that you don't quite see all the complexity involved. I'm not saying I see all of it, but I can see there is more to it than you think.
What about bacteria? Not only don't they don't often use sexual reproduction, so they don't need a pair of parents to produce offsprings, but they exchange plasmids and therefore DNA with little regard for species.
Plants are a complete mess of genome duplication, aneuploidy and whatnot. In these aspects, they are sort of scary to me.
Also, what about formation of a new species? Do you think there is a clean-cut time when they stop producing offspring? Also, what exactly do you mean by fertile? Where do you get a partner to test if the offspring is fertile?
These are just a few problems that came to my mind right away. I'm sure there's loads more. I'm afraid that the notion of well organised, easy to categorise world just doesn't match the real world. Species are more or less a continuum. Incidentally, so is life. We have no good definition fornlife either. Just use whatever definition is useful at the moment and don't forget to specify it when necessary.