The missing bit is culture: the concepts, expectations, practices, attitudes… that are evolved over time by a human group and which each one of us has picked up throughout our lifetimes, both implicitly and explicitly.
LLMs are great at predicting and navigating human culture, at least the subset that can be captured in their training sets.
The ways in which we interact with other people are culturally mediated. LLMs are not people, but they can simulate that culturally-mediated communication well enough that we find it easy to anthropomorphise them.