* The Moon orbits the Earth: A dwarf planet must orbit the Sun directly.

* The Moon doesn't meet the criteria for a planet: A dwarf planet needs to be in hydrostatic equilibrium (round due to its own gravity), have cleared its neighborhood of other objects, and not be a satellite of another object. The Moon meets the first requirement but not the other two.

In summary, the Moon is a natural satellite of Earth, not a dwarf planet.