The teaching says that What I Am cannot be disturbed. How can this be understood?

Objective experiences are (a) thinking and feeling (finite mind), (b) perceiving (the world), and (c) sensing (bodily sensation).

What I Am is not an objective experience. I’m the Unseen Seer (The Upanishads).

That is, I can never find Myself as an objective experience, as an object.

In fact, I’m aware of all objective experiences (without being any of them).

Consider:

They come and go; I do not come and go. That is, they change; I am changeless.

They are many; I am One.

A second pass: according to the principle of the indiscernibility of identicals, if two things do not share the exact same properties, then they cannot be identical. What I Am does not share the exact same qualities as any objective experience. Therefore, What I Am and objective experiences are not identical. (*)

Consequently, whatever happens to feeling (for example) does not apply to Me. Fear (for instance) cannot apply to Me.

Conclusion: I cannot be affected, impacted, or disturbed by any objective experience.

See this clearly.

Residing in this experiential understanding, I discover that I am Peace.

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(*) Ultimately, objective experiences are understood to consist only of Awareness. At this level of understanding (a provisional one canvassed above), it can be said that Awareness is different from objective experiences. This is an upaya, not the final truth.