/ wrote:"A species is often defined as the largest group of organisms capable of interbreeding and producing fertile offspring." -Wikipedia
That is often a useful biological (evolutionary) definition, but it should be easy to see why it fails when describing the characteristics of individuals. Is a human still a human if his or her genitals are removed? Or if he or she is born with a genetic abormality that prevents sexual organs from ever developing? Is a human still a human if he or she is in a permanent vegetative state and cannot physically engage in the act of copulation? I certainly think so.
I think that's a concise enough definition. If we also add the first generation offspring regardless of fertility, it would be enough to include all living modern day Homo sapiens. Even if my great-x-a-zillion-grand whatsit was a was a protozoa, it doesn't further my future genetic line. If you ever naturally impregnated an Orangutan, I would admit that they are humans. The same with lost Neadrathals, they might have been human in their time, but the moment their genetic line theoretically diverged enough to to become incapable in interbreeding, I would argue they became a competing species of their own.
I hope it was clear that I was making a distinction between biology and morals. Yes, you could run your experiment back through time and declare that the first organism you could not breed with, is a non-human. Now, this would still be impossible to do, because there would be an intermediate phase where the offspring are fertile but aren't exactly like modern humans, and it would progressively get more difficult as you went back. There would not be a daughter you could have fertile offspring with, while its mother was incapable of it. That is the point I was actually making when I said that the clear species definition is impossible.
But suppose you were successful anyway. Is "this is an organism that I can breed with" a meaningful moral statement? Of course not. Whether or not you can have a child with another human really has nothing to do with whether they deserve rights. That is why the moral concept of human is fuzzy -- any description of a human that actually captures what BBS (say) means by human must revert to biological truisms like "23 chromosome pairs," which raises the question of who the hell cares about the number of chromosome pairs you have. Humans deserve respect if they can feel pain and think, not because they're part of some arbitrary biological category.