. . . I am no marine biologist so I might be wrong, but I was under the impression that dolphins are part of the whale family, just a different branch than the "classical" whales like e.g. humpbacks?
They're all cetaceans, which comprise an order, not a family. Dolphins and porpoises are basically just small whales.
I see where the problem lies:
While both our languages divide the Order up into the two suborders Balean Whales (Mysticeti) and Toothed Whales (Odontoceti), we Germans follow that logic and call the whole order "Whales", while you instead use an anglicized version of the scientific name (Cetacea) : Cetaceans.
We both mean the same and only use different ways to express it. (We Germans try to avoid the use of scientific names as much as possible. It's mainly a matter of spelling and keeping words short, I suspect).
It's these tiny differences between our languages that drive people into despair (or into flame wars).