The way the illusion of “selfing” works is thusly: the brain processes information non-stop 24/7 and has to decide what is a threat and what is useful. But to whom is all this info. relevant to??
The answer is to the fictitious, purely mental “me” that I have mistakenly identified myself as. But, where did this “me” come from in the first place? Was it there at birth? No. It didn’t show up until around the age of 1-1 1/2 years old.
Once this sense of a separate self shows up, Consciousness automatically identifies with it, and our suffering/confusion/sense of separation/seeking begins. Thus, awakening is realizing that you, Consciousness, are intrinsically whole and cannot be this sense of separation, regardless of how “real” the illusion may feel/seem. Note that the brain did nothing wrong; if it wasn’t suppose to create this sense of a “false me,” it would not appear to happen.
Remember, an appearance is NOT the actual. The actual is changeless. An appearance changes, and thus cannot be your true nature. The good news is that just because an illusion arises doesn’t mean it can’t be seen through and recognized for what it is; an apparent modification of that which is eternally unmodifiable.
Michael Jeffreys
Michael Jeffreys 
Regarding the brain, you say: “if it wasn’t suppose to create this sense of a “false me,” it would not appear to happen”. Is a false self created by the brain?
If so, is this inevitable with everyone?
“Who” is asking?? Inquire.