In an optical illusion, we perceive something that isn't there due to exploiting a correction mechanism that's meant to allow us to make better practical sense of visual information in the average case.

Asking LLMs to count letters in a word fails because the needed information isn't part of their sensory data in the first place (to the extent that a program's I/O can be described as "sense"). They reason about text in atomic word-like tokens, without perceiving individual letters. No matter how many times they're fed training data saying things like "there are two b's in blueberry", this doesn't register as a fact about the word "blueberry" in itself, but as a fact about how the word grammatically functions, or about how blueberries tend to be discussed. They don't model the concept of addition, or counting; they only model the concept of explaining those concepts.