When is a whale not a whale? When taxonomy conflicts with everyday language.
According to the author of a recent article on the internet, “Although they’re called killer whales, orcas are not actually whales; they belong to the oceanic dolphin family, of which they are the largest members.”
That statement is both correct in that orcas are in the family Delphinidae, and also incorrect at a higher level—and such statements are ubiquitous on the internet. Using this logic, a goldfish is not a fish because it is a member of the carp family. You are not a placental mammal because you are in the family Hominidae. And roses are not plants because they are in the Rosaceae.
Carp are fish. Minnows are fish. Goldfish are fish. Placing species in family groups in manmade taxonomic schemes does not eliminate the larger more inclusive groups defining types of organisms. A goldfish is a cyprinid, cyprinids are a type of fish, and therefore, goldfish are fish.
Orcas presently are in the family Delphinidae. The family Delphinidae is one of many cetacean (whale) families. So by the transitive relations: orcas are whales.
Whales ultimately evolved from a group of terrestrial mammals, derived from synapsid reptiles, which evolved from amphibians, which evolved from lobe-finned fishes. So mammals, including whales, also are a subset of fishes, if we take this to a crazy extreme. I take great delight in being a fish and a Pisces—not that the present alignment of stars is an indicator of anything.