That is because you cannot do it yourself. Sorry, no other conclusion is possible from what you post.
Let me break it down a bit: There is non-general intelligence. You can fake that with tables and other preconfiguration mechanisms, because the domain and the set of conclusion is finite and known in advance.
On the other side, there is general intelligence. That one cannot be done with any precomputations. It requires the elusive quality of "insight" and that is whu LLMs can (provably) not do it.
In essence, what an LLM (and sadly many people) do is look up some precomputed "reasoning" and replay that. Many people do that without any fact-checking at all and what they arrive is called an "illusion of understanding". Also note that only about 10-15% of the human race are independent thinkers (i.e. able to fact-check), the rest does not actually have or use general intelligence. You seem to be in the 85...90%.