It should also be pointed out, this is not the first time a planet has been demoted.
Ceres was considered a planet, but when more objects started being discovered in the asteroid belt, the classification of asteroid was created, and Ceres lumped into it. Now that the dwarf planet classification exists, Ceres has been put in that category since it's the only object in the asteroid belt that's actually round.
The names, though are still somewhat arbitrary.
The reason for first classifying asteroids then dwarf planets is because originally planet just mean orbits the sun (or, theoretically any star, but only recently have we been able to discover objects orbiting other stars), but having thousands of "planets" would seemingly devalue the term given the importance we place on the objects currently defined as planets.
It's also notable that Ploto isn't defined as a binary since the barycenter is between it and Charon. Scientists can still be stubborn (of course, even that has problems, the Earth is slowly being tidally locked to the Moon, and as the rotational velocity decreases conservation of momentum increases the orbital distance of the Moon, so eventually the barycenter of the Earth-Moon system will be outside the Earth; would we then similarly define that as a binary system?)
