> If you want to educate, educate with precision, and don't spread your misinformation!

I would assert that the author was already being precise. A statement that X is "sometimes called" Y already conventionally carries the subtext that Y isn't actually the correct term; that Y is instead some kind of colloquial variant or corrupted layman's coinage for the more generally-agreed-upon term X.

Why mention the incorrect terminology Y at all, then?

Specifically in the case that pertains here, where far more laymen are already familiar with the Y term than the X term, giving Y as a synonym in the definition of X is a way to give people who are already familiar with this concept — but who only know it as Y — an immediate understanding of what is being discussed, by connecting their knowledge of "Y" over to the X term the author is defining. This is an extremely common practice in academic writing, especially in textbooks.