It is not hand-waving; it is the difference between an LLM, which, again, has no cognizance, no agency, and no thought -- and humans, which do. Do you truly believe humans are simply mechanistic processes that when you ask them a question, a cascade of mathematics occurs and they spit out an output? People actually have an internal reality. For example, they could refuse to answer your question! Can an LLM do even something that simple?
I find it absolutely mystifying you claim you've studied this when you so confidently analogize humans and LLMs when they truly are nothing alike.