IMO, what one needs to realize that the sense of ‘Self’ or ‘Me’ is an emergent result of a process of I- making and Mine - making, based on the underlying tendency to postulate an observer of any particular aspect of Experience whether internal or external (SN22.91).
This sense of ‘Self’ can be compared to a rainbow. It would be foolish to categorically deny the existence of a rainbow. Even saying that a rainbow is not real may not be easily acceptable to many (“What do you mean? I can see it right here! 
” ). However, the truth is that rainbows come about because of certain underlying conditions… when those underlying conditions cease, the rainbow disappears (MN72). The ‘Self’, just like a rainbow is not Really Real. Its an emergent phenomenon based on the functioning of an impersonal system of aggregates - in many ways like Siri!
The most difficult to let go of aggregates are the mental ones, especially Intentional Action and Consciousness. This is because it is difficult to imagine that these can be without an ‘Agent’. The ancients developed an entire system (Abhidhamma) to explain how ‘Mind’ works dependent on ‘cetasikas’. In much the same way, modern researchers talk about ‘Neural Nets’ and ‘weights’. None of these are permanent. None of these is one’s ‘Self’.
It is possible that viewing the ever changing Mindstream of past moments of Conscious Experience, one might think that this impermanent, changing process is somehow eternal/ constant (“Change is the only constant?!”). That too is not the case. Craving is the seamstress that stiches these moments together - when that is let go of, all that’s left is Now - Timeless, Deathless, the Supreme Sanctuary - Nibbana.