I don't see how the culinary definition of fish is related to cladistics.
Even if they were, I don't see what you dispute, because they agree on this point; if "vegetarian" means "avoid meat" and "meat" means "flesh of animal", then vegetarian also means to avoid fish. Come to think of it, eggs would also be included in that definition.
So from this I can tell that you're not one. Also, that you didn't get the joke.
I have been ovo-lacto-vegetarian for about 40 years now. So many self-identified "vegetarians" think that fish is vegetarian that many many restaurants etc. offer fish-based dishes as "vegetarian". I have frequently had to go totally without food because there was nothing available for me, because all the "vegetarian" options contained fish.
This is an extremely widespread issue, which you've never noticed. That's why you don't understand the relevance.
As for cladistics, again, this is very simple: look at the number of different types of animal that are called "fish".
. Shellfish (which includes crustaceans, i.e. arthropods, bivalve and gastropod molluscs)
. Hagfish (and lampreys)
. Starfish
. Jellyfish
Even going by simpler understandings: chondrichthyes and osteichthyes are both, to the general public, just "fish" with no particular distinction between these wildly different clades.
And this still overlaps with dietary restrictions. Kosher food excludes crustaceans but permits fish with fins _and_ scales, with a loose definition of both.
The public understanding of "fish" is a perfect example of the non-overlapping nature of the general understanding of groups of animals and plants, and the scientific one. The public understanding bears little more relationship to reality than Borges' classification in "The Analytical Language of John Wilkins" –
«
animals are divided into:
those that belong to the Emperor,
embalmed ones,
those that are trained,
suckling pigs,
mermaids,
fabulous ones,
stray dogs,
those included in the present classification,
those that tremble as if they were mad,
innumerable ones,
those drawn with a very fine camelhair brush,
others,
those that have just broken a flower vase,
those that from a long way off look like flies.
»
I have been. For instance, I was served trepang in a Chinese restaurant once. I asked what it was -- I wasn't veggie yet in those days, I was still just a kid. They told me it was a fish.
No Google in those days, so I had to go to the library and look through books, which told me it was a sea-slug. It's not.
It is of course an animal cell and demonstrates well the issues.
Hens lay eggs without copulation. These eggs are sterile: they cannot develop into an embryo and thus another hen. So, to some vegetarians, they are acceptable. They are non-viable.
But hens reared in the presence of a cockerel may well be fertilised, and thus viable, and thus not acceptable for very strict ovo-lacto-vegetarians.
Ducks, quails, and some other farmed birds, do not generally lay eggs unless they have copulated, and so their eggs are often not considered suitable for vegetarians.
Birds' eggs can be collected without harm or suffering to the animal; so, some vegetarians considera that fine.
But eggs of any type are quite definitely an animal product and so not edible by vegans, whether viable or not, fertilised or not.
Fish eggs are never suitable for vegetarians, because collecting them means killing the animal. This is a simple and obvious distinction but one that is not apparent to most non-vegetarians. So, no caviar, no fish roe, etc.
For the very strict, that also means not consuming a lot of beer, because it is fined with isinglass, a byproduct of killing fish. However, I know vegans who drink beer.
It is a lot more complicated than it appears to outsiders.
Even if they were, I don't see what you dispute, because they agree on this point; if "vegetarian" means "avoid meat" and "meat" means "flesh of animal", then vegetarian also means to avoid fish. Come to think of it, eggs would also be included in that definition.