The simpler and I think correct conclusion is that the LLM simply does not reason in our sense of the word. It mimics the reasoning pattern and try to get it right but could not.
Humans who fail to reason correctly with similar frequency aren't good at solving that task, same as LLMs. For the N-th time, "LLM is as good at this task as a human who's bad at it" isn't a good selling point.
I didn't but I'm happy to make that claim - humans who exhibit that sort of behavior aren't reasoning either, and they are just as unpleasant to deal with as LLMs are.