This is not a problem with AI, this is a problem with a human accepting an answer without understanding why it is correct. The tutor could also read a book that states "A square is not a rectangle" (or vice versa) and repeating it back to the student as established fact.

I am very curious what either person asked that led them to say that AI had told them a square is not a rectangle.

The obvious question of “is a square a rectangle?” is definitely NOT causing any LLM to say “no”.

Hallucinations are an issue but they genuinely are no longer a concern for any modern non-tiny LLM for basic facts that you would expect a K-6 course to cover. Maybe you might be able to find a few random hallucinations in knowledge covered at the high school level but I’m quite skeptical even that still happens. Yes, they can still, at times, hallucinate sources but I cannot recall the last time I actually saw this happen. I think it was at least a year ago

In what world is a square not a rectangle?

I don't understand how your wife interrogated the AI to be told a square is not a rectangle.

And how can two tutors disagree on this?

What kind of AI is this? ChatGPT says a square is a rectangle. Google search says it.

Let me say this in a different way: If some rectangles can also be squares, then this shows that a square is a rectangle. This is not a logical deduction; it is an intuitive one.