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.
»
https://multicians.org/thvv/borges-animals.html