The taxonomy of fish is often taken to be important and symbolic: how our intuitive taxonomic concepts are wrong, or why they should trump scientific results, or something about hubris, or how concepts construct reality. This all relies on the idea that modern phylogenetic methods have told us something deeply surprising, or even mysterious. We all think we know what fish are but, aha! fish are not even a real category. This means, for modern taxonomists, that they are not a clade. Some fish are more closely related to land animals than to other fish.
However, I think the results of modern phylogenetics aren’t surprising, if you know a little about fish. When most of us think of fish, we’re really just thinking of ray-finned fishes, Actinoptergyii, and Actinopterygii is a clade. It is a perfectly good taxon, intuitively and phylogenetically. The other “fish” are hagfish, lampreys, sharks & rays, and lobe-finned fish. If you have a mental image of a hagfish, compare that to your mental image of “fish”; if not, resort to google. Is it very surprising that hagfish are something different? Try the same for lampreys. Sharks and rays are well-known and also, I think, an intuitively obvious taxon. If you just looked out at the world of fish and started mentally grouping them together, I think you would pull these three groups out very quickly and naturally. Or maybe you would group hagfish and lampreys together, but still be certain that they aren’t in the same group as trout, sardines, and the like. The lobe-finned fish might not be as obvious. Coelacanths are famous for being weird, but if you saw a coelacanth or a lungfish it might fit well enough with your mental image of “fish”. If you start learning a little more about them, though, some obvious oddities pop up pretty quickly. Lungfish have, for instance, lungs. So it might be surprising for these to be a different group from our familiar ray-finned fishes, but not very surprising with a little knowledge.
The main surprise might be that lobe-finned fish are so closely related to land animals. And maybe you would have assumed that these five groups of fish all share a common ancestor–but I don’t really think phylogeny plays an explicit role in intuitive taxonomy except after long training. Your mental image of fish isn’t a phylogeny, it’s a mental map of similarities and differences between animals. And if that mental map is at all well-developed, it would already have most or all of the five clades within fish as well-developed, separate categories. The phylogenetic results are as much a confirmation of intuitive taxonomy as a rejection of it. You can phrase it to sound surprising–fish aren’t real!–or you can phrase it to sound unsurprising–did you know sharks are in a separate group from catfish? Framing it as a surprise makes for a more exciting story, of course, but it also draws a big line between what we think we know about the world and what people in labcoats tell us about the world. I think this is unhelpful, and anti-scientific even if not presented with that intent. Science is about understanding, but this framing tells us that there’s a gap between science and what we understand.