The most common argument for this is some core unexamined axiom that only humans can reason by definition, and then working backwards to a justification for that.
(I suppose a religious or otherwise superstitious person might introduce the soul into this, but I haven't come across anyone actually willing to defend that hill.)
The relevant MW definition for "reasoning" is: "the use of reason, especially: the drawing of inferences or conclusions through the use of reason."
And "reason" is: "the power of comprehending, inferring, or thinking especially in orderly rational ways."
Functionally speaking, i.e. in terms of observable behavior, LLMs exhibit comprehension, inferring, and reasoning. If someone wants to object to that, they'd need to explain what relevant property prevents a conclusion drawn by an LLM from being counted as involving reasoning.