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.
To be honest the impression I've gotten is that some people are just very interested in talking about not anthropomorphizing AI, and less interested in talking about AI behaviors, so they see conversations about the latter as a chance to talk about the former.
Outside the technical world it gets much worse. There are people who killed themselves because of LLMs, people who are in love with them, people who genuinely believe they have “awakened” their own private ChatGPT instance into AGI and are eschewing the real humans in their lives.