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.

Confabulations

People expect LLM mistakes be like human mistakes I guess

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.

LLM privileges.

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.

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.