I think part of the problem was that there was not a very careful definition of a planet.

People were basically saying that a planet was an object which orbited the Sun, but was not an asteroid or comet or something like that. When it became obvious that Pluto was a lot smaller than other planets and that it was just one of a number of similar sized objects out there beyond Neptune, some people started saying maybe we should not think of Pluto as a regular planet, but as part of a separate group.

Something like this happened before with the asteroids. Back when the first largest asteroids were discovered (like Ceres) people thought of them as planets, but then when it was realized that there were a bunch of relatively small objects in a similar orbit they decided to call them something else instead. There is an article about that here:
http://aa.usno.navy.mil/h...ry/minorplanets.html

Terry