For example, if you ask an llm a question, and it produces a hallucination then you try to correct it or explain to it that it is incorrect; and it produces a near identical hallucination while implying that it has produced a new, correct result, this suggests that it does not understand its own understanding (or pseudo-understanding if you like).
Without this level of introspection, directing any notion of true understanding, intelligence, or anything similar seems premature.
Llms need to be able to consistently and accurately say, some variation on the phrase "I don't know," or "I'm uncertain." This indicates knowledge of self. It's like a mirror test for minds.