Oh, but you should not classify living beings according to their habitat and behaviour; classification based on the degree of the phylogenetical relationship is obviously superior and the only truly reasonble one.
You should classify living beings according to a system that is helpful to understand and discuss the livings beings in a given context. "Fish" isn't a specific taxon in the standard biological taxonomy, but is rather a description of a specific set of common physical attributes and behaviors that is helpful to differentiate some organisms from other organisms. Regardless of official taxonomy, for 99.99% of people it's helpful to describe eels as fish.
Now, there’s something wrong with saying “whales are phylogenetically just as closely related to bass, herring, and salmon as these three are related to each other.” What’s wrong with the statement is that it’s false. But saying “whales are a kind of fish” isn’t.
