My favourite example is the "chicken and egg" problem. The difficulty of it is to define what a chicken is, everything is trivial afterwards. The answer, IMHO, is that "a chicken" was born from an egg put by a "non-chicken".
If you stack these pictures, there is no single picture you can pull out and say: "Here I transitioned from child to adult" e.g. Likewise with animals and evolution. Changes are so minute that you can speak of a transition from one species to another happening at the point of birth.
Only when you look at pictures of yourself far away from each other in the pile can you start differentiating them. Likewise with animals.
Under that definition, humans make a species. Horses make a species, donkeys make a species, but mules do not. Apparently in the world of Star Trek, Klingons and humans make a species: Worf (Klingon) had a child with a half-human/half-Klingon woman, and Tom Paris (human) had a child with a half-human/half-Klingon woman. Not sure about Vulcans and Romulans...obviously they can mate, but I'm not sure Spock himself can have children, perhaps we'll find out in a future movie. In Futurama, Kiff reproduced with Leela.
As to the concept of a human as a "super-organism", the problem with bacteria being part of the equation is that they do not transmit their replicator payload through the germ-line transmission vector. They are not integrated into the next generation in whole or in part. Via the concept of the extended phenotype they may alter and extend their environment to improve their chance of success (and often mothers and children have the same bacteria flora), but it's better to think of it as symbiosis (or in the worst case, parasitism) than true "super-organism" reproduction. (Me thinks!)
That's what we learned in high-school too, but as you mentioned, it doesn't make sense for donkeys, nor does it work for ring species[1], or organisms that reproduce asexually[2]. Mules can occasionally become mothers[3].
1. https://en.wikipedia.org/wiki/Ring_species
2. https://en.wikipedia.org/wiki/Asexual_reproduction
3. http://www.npr.org/templates/story/story.php?storyId=1226025...
Also, I hadn't considered to qualify "sexual reproduction", as asexual reproduction might be better thought of as strains (perhaps), the classification systems for simpler organisms tends to be more structural than fecund. In my defense, I tend to refer to organisms as assemblages of organs of which simpler biota can loosely be said to possess, though I always thought of the "organs" of single-cellular creatures as organelles as they are not made up of "tissue" as they are in multi-cellular organisms.
Rarely, sometimes mules are fertile.
And as far as humans, no one's entirely sure that chimps and humans aren't inter-fertile... at least at the level of horses/donkeys.
So for me rather than concepts like "species" being meaningless, they can have meaning (or at least value), but best not to think of them as iron laws. Mostly the point I was hoping to get to in my root response before I diverted myself reading my own text while typing it.
It's easier to create iron laws for categorical manipulation than it is to place observations into categories to begin with.
The thing about life boundries though in biology is that the more you know the less it makes sense. All bacteria are technically a single species, as are Archaea. Virus's aren't considered alive at all, though they do evolve. Then there are asexual creatures entirely. I vaguely recall a lizard that has no real genetic diversity because they are all females that reproduce without any sex, and there are no males. So... they're not a species either, but are still reproducing. Biology is screwy.
Post menopausal woman and some adult workers have both lost the ability to reproduce. But, they did have it in the past.
Which suggests the question; should we consider tribes a 'super' organism? As it includes and benefits from sterile members. What about things like monastic orders or wolf packs whose members forgo reproduction?
Newtonian physics are very useful and less blurry than reality.
More relevant, categories are useful and less blurry than reality. There doesn't need to be a sudden major difference between a chicken and a not-chicken. They only need to have a clear distinction in the model.
For comparison, let's look at integers. 11 is very similar to 12, and 13 is at least as similar, but 11 and 12 are not-teen and 13 is teen. There's no ambiguity, there is only the definition of the category/model "teen".
The distinction is arbitrary, but there's still a distinction. You can easily "draw a line" as the sibling comment says.
And the thing is, you could not determine when exactly the non-chicken became the chicken i.e. when it is chicken enough. You could not draw a line.