The discussion centers on the misconception that particles can exist in two mutually exclusive states simultaneously, which contradicts experimental results indicating that measured outcomes do not reflect superposition states. It is emphasized that for observables with a finite discrete spectrum, there are a limited number of possible outcomes, and superposition does not imply simultaneous existence in multiple states. The conversation highlights the importance of understanding vector spaces and the distinction between states and observables in quantum mechanics. Participants argue that a state vector can be expressed in different bases, but this does not mean the particle is in multiple states at once. Overall, the claim that particles can be in superposition of mutually exclusive states is deemed incorrect and misleading.