Neither can you easily notice that when a human teacher/tutor does that. At least with math, you're able to try it yourself and see if it works. I've had many cases where following through on a misleading explanation by a teacher/book actually ended up leading to me better retaining the topic.
That's absolutely a bug that needs to be fixed, but I think it's possible. Maybe have the network which generates the answer be moderated by another network that assesses the truthiness of it.
It's just a matter of priorities for the company designing the models.
Especially in a limited domain like grade school math, it seems entirely plausible that we can have models in very short order that ~never hallucinate. There's no external dependencies and the problem space is extremely well-defined and constrained. Much, much, much easier than making something like Chat-GPT never hallucinate