You are almost there in terms of getting their point, so I will explain.
Birds existed since forever ago in nature, and they fly by flapping their wings. Then planes got invented, and they fly using a very different mechanism (that doesn't involve flapping wings).
The point made by the grandparent comment: saying "LLMs don't actually reason, because the underlying mechanism they use is different from how humans reason" feels about the same as "planes don't actually fly, because the underlying mechanism they use is different from how birds fly".
Birds existed since forever ago in nature, and they fly by flapping their wings. Then planes got invented, and they fly using a very different mechanism (that doesn't involve flapping wings).
The point made by the grandparent comment: saying "LLMs don't actually reason, because the underlying mechanism they use is different from how humans reason" feels about the same as "planes don't actually fly, because the underlying mechanism they use is different from how birds fly".