Worth noting that Atomic Habits does _not_ say what you are suggesting here, it says to create a new identity (I am someone who exercises) then prove to yourself that that is true. It does not suggest to internalize it and hope action follows, or to internalize it and attempt to convince others.
The helpful suggestion of Atomic Habits is that instead of saying "I am someone who exercises" and setting a goal of running a marathon, you just go out for a run, or a walk, of any length until you've proven, again to yourself, that this is a habit you are going to keep.
The helpful suggestion of Atomic Habits is that instead of saying "I am someone who exercises" and setting a goal of running a marathon, you just go out for a run, or a walk, of any length until you've proven, again to yourself, that this is a habit you are going to keep.