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.
Whether it's hallucinations, prompt injections, various other security vulnerabilities/scenarios, or problems with doing math, backtracking, getting confused - there's a steady supply of "problems" that some people are surprised to discover and even more surprised this isn't being definitively fixed. Thing is, none of that is surprising, and these things are not bugs, they're flip side of the features - but to see that, one has to realize that humans demonstrate those exact same failure modes.
Especially when it comes to designing larger systems incorporating LLM "agents", it really helps to think of them as humans - because the problems those systems face are exactly the same as you get with systems incorporating people, and mostly for the same underlying reasons. Anthropomorphizing LLMs cuts through a lot of misconceptions and false paths, and helps one realize that we have millennia of experience with people-centric computing systems (aka. bureaucracy) that's directly transferrable.