"Teaching" by copying source books word for word, would be copyright infringement; see, for example, the well-known issues around photocopying books or even excerpts.
Also lying on source materials (e.g. telling students that some respected historian denies the Holocaust happened, when it's obviously not the case) is not "teaching" - it's defamation, and the NYT is absolutely right to pursue that angle too.
Using LLMs as general-purpose search engines is a minefield, I would not be surprised if the practice disappeared in the next 20 years. Obviously the tech is here to stay, there is no problem when it's applied to augmenting niche work; but as a Google replacement, it has so many issues