6 ideas
Zhuang Zhou dreams he is a butterfly, flitting about content and wholly unaware that he is Zhou. He wakes, suddenly and solidly Zhou again, and cannot tell whether he is Zhou who dreamt of being a butterfly or a butterfly now dreaming of being Zhou. The story settles nothing. It only leaves the reader in the same uncertainty Zhou woke into.
Inside the dream, the butterfly's experience felt complete and self-evident, with no trace that it was a dream. Waking brings the same felt certainty, so the vividness of a present state is no evidence that it is the real one. The two states cannot be compared from some third, neutral position, because every judgment is made from inside one of them.
Zhuangzi ends the parable by saying there must be some distinction between Zhou and the butterfly, and that this is called the transformation of things. The distinction is real, but it marks a passage between forms rather than a fixed boundary around one true self. Identity becomes a stage in an ongoing change rather than a substance that persists through change.
The butterfly is not a lesser Zhou and Zhou is not a failed butterfly. Each form is fully content within its own frame and does not need the other. This way of seeing takes away the reason to rank states of being against each other or to cling to the current one as the privileged one.
Zhuangzi does not collapse Zhou and butterfly into one, and he does not declare the difference an illusion. He holds that the distinction is real and that he cannot determine which side he stands on. You can grant that differences exist without having a vantage point from which to locate yourself among them.
If one waking turned out to be another dream, then no present awareness can be assumed to be the final one. Treating your current certainty as possibly a dream from which you might still wake keeps judgments held loosely.