I can agree that not calling it "reasoning" may be correct.
But who knows what human "thinking" is really about. If I find a solution to something it is seldom by painstakingly tracing that A and B leads to C (for that I'd need pen and paper). Rather, thoughts just swirl around and then suddenly a solution, or a hunch about a direction to go in, pops into my mind. Who knows what such thoughts "look like" in humans. It is not all of it I can introspect.
Yes I can sort of follow along some kind of train of thought in my head, but there's a lot going on between each thing I'm consciously aware of that I'm not aware of at all, which probably dominates what you are consciously aware of. (Humans are experts at post-rationalization and so on.)
I see this pattern a lot in AI anthro discussions: (1) Assume humans are some kind of perfect idealistic reasonable beings. (2) Hold LLMs up to the standard of an perfect idealistic reasonable being. (3) Conclude that LLMs fails this test, and are therefore not "intelligent", or in this case "thinking", like humans are.
Problem with the argument is comparing humans in anyway to something that is idealistic, reasonable, intelligent in the sense that is implied in these discussions. Human minds are a mess too and fall short of the same standards, just in very different ways from LLMs.
Indeed, except for in the rare cases we painstakingly trace externalised logic we have zero evidence that humans verbalised explanations of our reasoning matches our internal states either, and plenty of evidence via Sperry's split brain experiments that we're prone to outright making up rationalisations for our reasoning.