I mean, that’s a good analogy, the term “fish” is even worse than “race”. Fish is paraphyletic, just like “tree”. There’s also the colloquial sense of “fish”, which is even less clear.
In casual speech, you can certainly look at an animal and say "this is a fish", or look at a plant and say "that is a tree", but if you actually start to look closer, you find that there's no clear way to define either of those terms that includes everything we think should belong in them, and also excludes everything we think shouldn't.
"Races" among humans are similarly hard to pin down by any kind of genetic taxonomy.
science is for describing what is, and in detail, but science's failure to do that just means we need more science, not that we should quit and claim the above words have no meaning.
Proves too much: the idea of coming up with a genetic basis for "fishness" is also now completely useless.