You can also teach humans science and math and then they can be trained by a cult to not use any of that reasoning when emitting canned responses that they were rewarded by the cult for internalizing during their training. "Fake News!"

You're caught up on the mechanics of token processing (floating point matrix ALU math) and ignoring the context that p(next token) as a function being "computed" is doing so over a trillion parameters. You can poorly train a model, sure, but assuming you don't indoctrinate it too much, properties like cognition emerge - it learns to reason; why? Reasoning is more efficient and compact than memorizing answers.