The argument is very much inflicted with the bike-shed disease, largely because memorizing the planets is a common school activity so everyone feels they have a stake regardless of their scientific understanding of the subject.
The basic problem is that the definition of a planet has transitioned over time, a lot of time, from a colloquial definition to a scientific one. For the longest time "planet" was just a name for any large, permanent part of the solar system that was worth memorizing. Initially even the Sun and Earth's moon were planets, but the heliocentric revolution placed the Sun in a different category and inadvertently relegated the moon to a minor body along with all the other moons (notable only due to its proximity to human civilization). For a few decades the first 4 discivered asteroids were planets, but the discovery of hundreds and then thousands of similar asteroids brought the realization that these 4 bodies were not quite as notable as once thought. Pluto lasted much longer as the only known KBO for the better part of a century and thus snuck into planet hood.
When Pluto was alone it was much easier to ignore its differences and just chalk it up as the quirkiest member of the planets despite its tiny size, eccentric orbit tilted to the ecliptic, etc.
As we've discovered more planets in other systems and as we've discovered more objects in our outer solar sytem a firmer definition of planet has become more necessary. The new criteria for planet hood are straightforward and useful in understanding the nature and evolution of planetary systems. However, Pluto doesn't satisfy them. In scientific terms this isn't a big deal, but for the public and for the colloquial definition of planet there is still a lot of resistance to change.
Take a proto-stellar nebula, it's a big mass of gas and dust thousands of AU in diameter. Each particular bit will generally be moving very slowly in a random direction relative to the whole but the whole thing has some particular net angular momentum. As the nebula collapses to form a star this angular momentum gets concentrated (insert standard ice-skater pulling in their arms description here), which is why stars tend to have some particular spin. The same mechanism of concentration works to help form a protoplanetary disc. Objects in eccentric orbits or orbits tilted to the average plane of the forming disc will be more prone to collisions, causing them to be absorbed or captured by larger bodies or to form a debris cloud of generally lower eccentricity and lower inclination.
Over time these effects add up to cause most of the mass in the inner Solar System to be concentrated in a small number of planets in circular orbits within a narrow range of inclinations.
Note that in the far outer Solar System of the kuiper belt and oort cloud these effects are much diminished (orbital periods are much longer, distances are much larger, overall volumetric mass densities are lower, etc.) so objects are more likely to have eccentric and inclined orbits relative to the inner solar system consensus.
I get most of that, just not how it ends up in a flat disc. as opposed to an array of discs or something similar.
Is the idea that if you took the nebula, and measured across in 1 deg increments, the plane that had the largest percentage of largest objects is the highest probability of becoming the eventual plane?
This seems like the sort of concept that could do with a nicely done animation to explain.
The basic problem is that the definition of a planet has transitioned over time, a lot of time, from a colloquial definition to a scientific one. For the longest time "planet" was just a name for any large, permanent part of the solar system that was worth memorizing. Initially even the Sun and Earth's moon were planets, but the heliocentric revolution placed the Sun in a different category and inadvertently relegated the moon to a minor body along with all the other moons (notable only due to its proximity to human civilization). For a few decades the first 4 discivered asteroids were planets, but the discovery of hundreds and then thousands of similar asteroids brought the realization that these 4 bodies were not quite as notable as once thought. Pluto lasted much longer as the only known KBO for the better part of a century and thus snuck into planet hood.
When Pluto was alone it was much easier to ignore its differences and just chalk it up as the quirkiest member of the planets despite its tiny size, eccentric orbit tilted to the ecliptic, etc.
As we've discovered more planets in other systems and as we've discovered more objects in our outer solar sytem a firmer definition of planet has become more necessary. The new criteria for planet hood are straightforward and useful in understanding the nature and evolution of planetary systems. However, Pluto doesn't satisfy them. In scientific terms this isn't a big deal, but for the public and for the colloquial definition of planet there is still a lot of resistance to change.