The differentiation you've linked is about meat vs seafood, which I would go along with. This is about using the term "animal" for fish, no?

Here's an experiment I performed, you can try it if you care to. I just went to my preferred search engine and did an image search for "animal".

I had to scroll down about thirty images to find something that wasn't a mammal. It was a lizard. Most of the animals were fuzzy. (I may have missed some marsupials, to be fair.) I believe these search results are reflective of what people are looking for when they search "animal," and it isn't fish.

Are fish animals? I would agree. Is it normal to feel differently? I believe so.

You have to go down pages and pages to even find a hedgehog, and you find very few birds. I think you find very, very few people who wouldn't call an ostrich or a hedgehog an animal, so I don't know how much that experiment says really.

Why would you need to know anything about taxonomy in order to know fish are animals? Sorry, but no one I've ever known has made any distinction between the two.

I think maybe there is some overlap with op and the idea that "fish" is different from "meat." That's something that basically everyone said at some point.

Fish and animals are taxonomic categories (as are meat and fish, the food).

If fish aren't meat but are animals, it should tell you how arbitrary these distinctions are.

Fish is meat. It's just that people are used to associating "meat" with "red meat". But if you press people, they are not going to say that in no way is fish flesh considered meat. They just don't generally use the same word to describe both things.

You don't need to know any details of taxonomy as a discipline to know that fish are animals.

For the record, the original meaning of "meat," was just food, in general. So we have sweetmeats, mincemeat, etc.

The exercise you're talking about, is an exercise in taxonomy. (Though I agree it doesn't require special expertise to engage in taxonomy.)

It only requires a working brain to look at two similar things and categorize them similarly.