Eels are fish

Apparently we are all fish. Or fish don't exist.

To explain: if you want to define a taxonomy in which all things that look like fish and swim are 'fish' then we are too. We are more closely related to most 'fish' than sharks are. I.e the last common ancestor of herring AND sharks is older than our & herring's LCA.

Fish exist, and we're not fish. Fish just isn't a monophyletic taxonomic category. If you allow "fish" to be a list of all those animals that look like "fish" and swim like "fish", you'll end up with a bunch of animals who's most recent common ancestor is also the most recent common ancestor of all tertrapods (including humans), so "we are all fish". But if you don't demand a single common ancestor & instead just have a list of several different taxonomic classes you can define "fish" as anything in the list, thereby excluding humans.

It's like the difference between culinary berries (sweet parts of plants) and biological berries (parts of plants containing the seeds internally). Tomatoes are not a culinary berry, but are a biological berry. Strawberries are a culinary berry, but not a biological berry (the seeds are on the outside). It's confusion caused by mixing a jargon use of a word with the common use of that same word.