The thing is, there is no real evidence to back up the classification. The assignment between words and objects is arbitrary. A consistent definition for "planet" can be given and immediately after define the Solar System as being comprised of nine planets, with the understanding that a "planet" and a "planet of the Solar System" are similar but distinct concepts. The same is already done in biology with paraphyletic groups, with for example "reptiles" not including birds.

(I say this as someone who doesn't care either way whether Pluto is a planet or not.)