The language of "generator that stochastically produces the next word" is just not very useful when you're talking about, e.g., an LLM that is answering complex world modeling questions or generating a creative story. It's at the wrong level of abstraction, just as if you were discussing an UI events API and you were talking about zeros and ones, or voltages in transistors. Technically fine but totally useless to reach any conclusion about the high-level system.
We need a higher abstraction level to talk about higher level phenomena in LLMs as well, and the problem is that we have no idea what happens internally at those higher abstraction levels. So, considering that LLMs somehow imitate humans (at least in terms of output), anthropomorphization is the best abstraction we have, hence people naturally resort to it when discussing what LLMs can do.
Long before LLMs, I would talk about classes / functions / modules like "it then does this, decides the epsilon is too low, chops it up and adds it to the list".
The difference I guess it was only to a technical crowd and nobody would mistake this for anything it wasn't. Everybody know that "it" didn't "decide" anything.
With AI being so mainstream and the math being much more elusive than a simple if..then I guess it's just too easy to take this simple speaking convention at face value.
EDIT: some clarifications / wording
Maybe it's cog-nition (emphasis on the cog).
I think the above poster gets a little distracted by suggesting the models are creative which itself is disputed. Perhaps a better term, like above, would be to just use "model". They are models after all. We don't make up a new portmanteau for submarines. They float, or drive, or submarine around.
So maybe an LLM doesn't "write" a poem, but instead "models a poem" which maybe indeed take away a little of the sketchy magic and fake humanness they tend to be imbued with.
We're very used to "all models are wrong, some are useful", "the map is not the territory", etc.
Ties in with creation from many and synthetic/artificial data. I usually prompt instruct my coding models more with “synthesize” than “generate”.