On occasion I have argued that dolphins are fish, despite being air breathing mammals, using an argument quite similar to this. The use of the word 'fish' to describe animals that live in the water predates biologists deciding they'd redefine the term unilaterally for the rest of society. The novel Moby Dick explains in detail the difference between whales and true fish, but then calls whales 'fish' in the rest of the book anyway.
If this line of argument doesn't work, I point out that in a phylogenetic/cladistic nomenclature, all tetrapods are fish and dolphins are tetrapods, therefore dolphins are fish (and so are we.) Of course in the traditional nomenclature 'fish' is a paraphyletic group that specifically excludes tetrapods.
> The novel Moby Dick explains in detail the difference between whales and true fish, but then calls whales 'fish' in the rest of the book anyway.
To add a more scientific example, "The Biology and Ecology of Giant Kelp Forests" (2015) similarly begins by explaining that kelp are brown macroalgae belonging in the kingdom Chromista rather than Plantae, and are thus is not technically plants. They then explain that they will call them plants anyway for the rest of the book.
It is, by the way, a surprisingly interesting book. Kelp was vastly more important between 150-100 years ago, and the science occasionally dips back to the scientific age of wonder of the late 1800s. (I always enjoy reading the classic papers from those times. They're written completely differently from modern scientific papers. Much less formal.)
If this line of argument doesn't work, I point out that in a phylogenetic/cladistic nomenclature, all tetrapods are fish and dolphins are tetrapods, therefore dolphins are fish (and so are we.) Of course in the traditional nomenclature 'fish' is a paraphyletic group that specifically excludes tetrapods.