They can, at times, and do so best when emotion is not involved.

> I'm tired of reading comments from people who keep repeating that LLMs don't think, don't reason, isn't intelligence because it is not human.

LLM's represent a category of algorithm. Quite elegant and useful in some circumstances, but an algorithm none the less. A quick search produced this[0] example discussing same.

Another reference, which may not be authoritative based on whatever most recent edit the link produces, is[1]:

  A large language model (LLM) is a computational model
  capable of language generation or other natural language
  processing tasks. As language models, LLMs acquire these
  abilities by learning statistical relationships from vast
  amounts of text during a self-supervised and semi-supervised
  training process.

Reasoning was the process I went through to formulate this response, doing so with intent to convey meaning as best as I can, and understand as best as possible the message to which I am replying.

> Then tell us why LLMs don't reason and why it matters.

LLM's do not possess the ability to perform the process detailed above.

This is why it matters.

0 - https://github.com/rasbt/LLMs-from-scratch

1 - https://en.wikipedia.org/wiki/Large_language_model