Because the Earth is so much more massive than the Moon, this point is beneath the surface of the Earth. Pluto and Charon, however, are different. They are so close in mass that the center of their masses is in the space between the two. This is radically different from every other planet in the Solar system. At the very least, it argues for Pluto and Charon to be considered a binary planet system, two gravitaionally-tied planets in the same orbit, instead of a single planet and a moon.
Tradition seems to have won out over standards of nomenclature for now.
Under public pressure, the IAU voted to continue to grant Pluto status as a planet. Pluto is the only known planet that has not yet been explored by unmanned spacecraft. We speak of aphelion in terms of planets orbiting the Sun, moons orbiting their planets, and especially artificial satellites orbiting the Earth. Kuiper refers to the Edgewordth-Kuiper Disk, a recently discovered ring of icy minor planets that orbit the Sun beyond Pluto.