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.