My guess is that they do so in imitation of humans who do the same thing when asked the sorts of questions that people ask LLMs. It's not an LLM thing; it's a thing one does to make distinctions clear, when the other person might otherwise conflate two distinct entities, clusters, or topics. It just so happens that people ask LLMs a lot of that sort of question, and thus elicit a lot of that particular response.
(I also use em dashes, yes.)
There seem to be common patterns of how LLMs write text that's shared by the LLMs of different companies and where the language patterns the LLM uses are different from usual human writing.
How much do we know about why LLMs pick certain patterns? Do we know why they use "It's not a X, it's an X" so often? If not, maybe understand why they pick patterns like it can make us better understand how LLMs are reasoning?