Do some people not feel this way at all times? Personally i always feel like my body isn't "me", it's just the functional shell that I'm living in. Like when i get in a car and go driving i don't feel like the car is me, it's just the functional shell I'm inside of. "Me" is my subjective sense of consciousness.
When i look in the mirror i mostly see it in the 3rd person. I see my face and i think "hey look at that guy", and "that face could use a shave", etc.