It’s important to understand “self” in the term “not-self” as meaning any possible way of defining your self, because no matter what “I” or “my” you come up with, you’re going to cling to it. The Buddha wants to help you to put an end to every possible way of clinging.
Ṭhānissaro Bhikkhu (1949-), Ṭhānissaro Bhikkhu is an American Buddhist monk. Belonging to the Thai Forest Tradition.