In the early 2000's as we started discovering additional large objects in the outer solar system, astronomical displays started to clump these objects in with Pluto. The rate at which we were discovering them made it seem likely that there would be many. And who wants to memorize 30 different planets? Which if you're lazy and don't want to be embarrassed when little kids know all the planet names but you, who are the actual astronomy professional, don't, means that Pluto has to go. That's it. Don't be fooled everything else is just a smoke screen. Pluto had to go so that a bunch of people who were full of themselves wouldn't have to keep memorizing new lists of planets that might subtly change order. Think about how often these same people, who should know very well that Pluto has a trans neptunian orbit, refer to Pluto as being beyond Neptune.
There is a case for Pluto's demotion. We didn't know how big it was when we discovered it. We thought it was bigger. We didn't know it was in a belt of objects, some of which were big. After it was discovered Ceres was briefly considered a planet, until we realized that it was part of a belt. And while it remains the largest and the only one large enough to pull itself into a sphere, it remained demoted to the rank of asteroid, until this whole kerfuffle, so again there was a reason to be considering these things.
But at the same time as we were finding new things in our solar system we were finding "Planets" in other solar systems, and even looking for ones that weren't captured by a star, that are called rogue planets. This is the back drop of the state of the art science at the time. We were looking for bodies outside of our solar system that didn't orbit stars that we were calling rogue planets. Remember that cause I'm going to come back to it. Also it's very possible that in other start systems we will find bodies in all sorts of exciting and strange orbital configurations.
So with a reason to consider the designation of things in our solar system, and the desire to limit how often school children embarrass them, the IAU set out. The definition that they cam up with is "(1) A planet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit".
Of the planet definition criteria b is a reasonable criteria. It is a clear dividing line that objects throughout the universe will be on one side of or another, and as such will be useful with all the extra-solar astronomy that is going on as well as with what's going on in the Solar system. This criteria is very broad though and in addition to what had been considered planets before it also captures stars and many (but not all) of the moons in the solar system.
Criteria a defines planets as being only in orbit around the Sun, and as a consequence there are only planets in our solar system. No extra solar planets, no rogue planets. Planets are just something we have. This is rubbish of course. Further it is complicated by just what that means. In orbital dynamics there is something called the Hill sphere, which is used when looking at two bodies to see if objects nearer the smaller one are orbiting it or the larger one. Right now the moon is orbiting the Earth, and the Earth the Sun. As little as ~1.27 million years ago when the moon was closer, the earth orbited the moon not the sun. Without wanting to do the math I would guess that for Pluto and Charon it is the case that they orbit each other and it's only their system that is in orbit around the sun. So this is the sort of things we should expect to see out there, so if we apply this definition to other systems and other suns it still will eventually break. This criteria wasn't forward thinking towards improving a definition for science. It's stated really naively so you have to guess that they are talking about Hill sphere's for the criteria, otherwise everything in the system orbits the sun. Also this criteria is part of the dwarf planet definition, so if Pluto and Charon are in orbit around each other then they are not even Dwarf Planets, or the framers we being even more naive and less scientific than that.
After what I did to criteria a, I'm sure that you are expecting that I think criteria c is a pure mess. It is. It's so bad and so naive that people keep coming out with "interpretations" of it, to fix the problems. So let's begin with the big one. Pluto and Neptune. Pluto crosses Neptune's orbit. How can you have cleared your orbit when there is something that big that crosses it? Then you have things like Earth and Cruithne, an asteroid in a 1:1 orbital resonance with the earth that crosses our orbit but isn't technically in orbit around us. And add on to that trojans. The original trojans were in Jupiter's orbit, but it's such a thing that we've generalized the term for all the planets, and they are objects in the same orbit, at the same orbital period, that are in the right spot to roughly never get cleared out of an orbit by a planet. That's right we know, and knew when the definition was made, that no planet could completely clear it's orbit. This definition is a lie. It's a lie that was put in place to kill Pluto and keep the rest of them out. And beyond the problems in our solar system there are lots of possible interesting orbital dynamics that we might find out there, that won't fly with this either. Sure a lot of them won't be super stable, but what's the threshold of stability? Nothing in our solar system is actually stable, so it can't be forever, and then after that you let in a lot of interesting things that we are going to find out there.
So the current definition is unscientific and garbage. As such I refuse to accept it. And revert to the previous state in which Pluto was a planet. If some one tries to argue for the demotion of Pluto, there is a simple question you can use to break them, "What is the difference between a rogue planet and a rogue dwarf planet?". You don't have to give them anything harder to think about than that question which the framers of the new definition, left unanswerable, which counter to the mandate for even considering the definition. In response to searching for and finding lots of new things they revised the definition to not be applicable or otherwise be nonsense to the new? No. Just No. If a future definition gets put forth that's good and demotes Pluto, I'll accept it. But I refuse to accept that trash just like I refuse to accept other garbage that wants to claim to be science.
What is required for a good definition? It has to consider all the types of things we're looking for, so it should consider objects in other sun systems as well as those in between them. It should be based on the intrinsic properties of a body not extrinsic ones. We're not going to have perfect knowledge of everything in a solar system when we first see a body, so it's designation shouldn't rely on other bodies that aren't clearly playing a major role in what's happening with that body. Also the definition should be very specific. It should start as a hard computable thing that is technically precise that can be summarized for humans, rather then something naively high level that might melt down when you actually get into the details.
I don't know if a body will ever put out a good definition that takes off. But I have some predictions. I predict that we'll define some new term like planetoid to account for objects between solar systems. Of objects that pull them selves into spheres, I think the divisions are more like to keep Pluto with Earth, than Earth with Jupiter. I think that after we define terms like planetoid (potentially with sub groupings) we will then define planet and moon based on orbital relations so that the Earth and the Moon can be the same type of object but will also have terms to describe them in terms of a start system. (I think moon and satellite will be split in this situation). And I think that in systems of mutuality like Pluto and Charon, the two are likely to hold the same status.