Essential Teachings of the Buddha: 'Not-Self' (Anattā) - Ajahn Dhammasiha
Ajahn Dhammasiha points out that the Buddha did not teach Not-Self to establish a theory or philosophy. The Buddha is not concerned with theorizing or arguing about philosophical views. His one and only concern is to get us out of suffering (dukkha); to teach us to end ageing, sickness, death and new rebirth; how to end all disappointment, frustration and pain. Not-Self if a meditative tool to achieve that through letting go.
The Buddha explains that we actively create the delusion of Self, we generate the attitude of possessiveness, we regard things as me, mine and Self. Ownership can not be determined 'objectively', but we subjectively project it into our experience.
The Buddha shows, however, that any such projection and delusion of me, mine & Self will ultimately create disappointment and suffering for us. The point is not to argue whether there's a Self or there's no Self. The point is what is the result of regarding things as self and mine. And that result is always suffering in the end.
Once the mind can clearly see and understand that regarding form, feeling, perception, intention and consciousness results in suffering, then the mind will let go as a direct consequence of that insight, and our suffering will end.