Is indeed whatever you observe cannot be you?
One of the core premises of spiritual inquiry and awareness is that whatever you observe cannot be you.
This is the basic idea behind the important process of peeling from your inflated "I" all the mental objects you identify with. It is tightly related to the formless nature of the "I", to the meaning of the minimized subject / center that observes.
Yet, although this claim is such a basic foundation block in spirituality, it is usually taken for granted, hardly ever questioned or reasoned.
Mooji addresses this claim in very nice allegories to a knife that cannot cut itself and a scale that cannot weight itself:
You are total unicity beyond duality. That you are. You are so one with yourself that you cannot perceive yourself. You can only imagine that you are other than that. It is like a knife that can cut so many vegetables but cannot cut itself because it is one with itself, or the scale which can weigh so many objects but cannot weigh itself. It is the same with the one supreme Self- the sole Reality, being ever One with itself, it cannot perceive that which it Is; it can only perceive what it is not.
For those who look for some intuitive or logical proof for this claim, I don't think you will be able to come up with a such (and if you can, please post it here in the comments). This claim is the rock bottom of spirituality. You will not be able to find a logical explanation and reasoning for this claim as it involves the observing subject while the mind can deal only with objects.
But still you are not asked to believe in it blindly. You can validate it by personal experience. The claim that whatever you observe cannot be you is clearly validated in personal practice when you meditate and observe mental objects - at some point you find yourself mentally separate from the object you observe.
For example, observe your body, observe the sensations, the hair that grows, by its own volition, on your skin, the movements, the pulsations. At some point a clear (sometimes fleeting) feeling will dawn on you: this body is not me. It is not an intellectual understanding, it is some clear mental understanding. Don't push it, don't expect it to happen, it will happen by itself, you just do the observing.
Lastly and interestingly, "whatever you perceive cannot be you" is one of the things that differentiate spirituality from science. According to the basic axioms of science, an entity can perceive itself as part of a relation called "reflexivity" of an element and itself.