Because LLMs don't think, and a mistake implies logic. "Hallucination" is an attempt to differentiate the problem and further emphasize its lack of basis in reality.
Words are inexact abstractions, and meanings change over time. If they can't think, how can they even hallucinate? Remember the old definition of "computer", and how its usage shifted from humans to man-made machines. I just think that "mistake" is a better analogy than "hallucination": It gives a result that does not concur with our shared experience of reality, like shifting signs on a maths exam. The human shifting sign is most probably not hallucinating. The human is making a mistake.
Because it sounds better. Mistakes and lies are something bad and suggest a company spreading them might do something bad. Hallucinations sound like something else.
A hallucination is a specific kind of mistake. There are also other kinds of mistakes LLMs can make; for example, they can draw incorrect conclusions from accurate information, or they can fail to find information that they "should" know.
Is claiming that the year when the orange man first came into office a mistake, or a hallucination? Does the answer change based on whether it came from a human or an LLM?
How about citing legal cases that don't exist? I would say this is maybe closer to hallucination if an LLM is doing it. Maybe less so if a human is and is not experience some mental instability. What creates that distinction?
I read a paper once (https://pmc.ncbi.nlm.nih.gov/articles/PMC10619792/pdf/pdig.0...) arguing that "confabulation" would be a more accurate term because it better matches the similar failure mode in humans, and perhaps that's true. It's just not the term that's won out. That may change, or psychologists may have to adopt a new term for what we currently call human hallucinations, the same way they had to develop a new term for what we used to call imbecility.
I believe the word comes from when people started using CNN models in reverse, so hallucinate input that never existed. LLM output is produced via a vaguely similar process. https://en.wikipedia.org/wiki/DeepDream
But in any case, they aren't mistakes. LLMs are not trained to produce true output; they are trained to produce likely output. "Likely" happens to overlap with "true" a lot, but not always. If you ask Claude why aeroplanes fly it will still spew some nonsense about curved wings. Very likely output; not really true.
LLMs are trained on a model of the world. We rely on them to produce output that correlates with our experience of the world. When we talk about truth, which is simply a word in language with various connotations, and which is a word that is very difficult to define objectively, we talk about what correlates (likeliness) with our shared experience of the world. LLMs have an internal model that is derived from experience, and so do humans.