Why is Pluto no longer considered a planet?

The main factor that drove the 2006 downgrading of Pluto from full planet status was not any change in Pluto itself, but rather a change in the definition of the word 'planet', from a scientific perspective. When Pluto was discovered, in 1930, it fit the criteria for planetary status in that it was round and orbited the sun. However, in 1992, Jane Luu and David Hewitt discovered a number of Trans-Neptunian Objects orbiting beyond Neptune, and in 2003, it was identified that at least one of these objects had a greater mass than Pluto. This prompted the International Astronomical Unit (IAU) to begin formally rethinking what constitutes a planet, and in 2006, they issued a new set of rules. For an object to constitute a planet:
1. It must be round 
2. It must orbit the sun
3. It must 'clear the neighbourhood' of its orbit -- that is, it must have sufficient gravity to clear the space around it of other objects as it travels. 
Pluto satisfies rules 1 and 2, but not rule 3. As such, it is now defined as a 'dwarf planet', of which there are currently five in our solar system. 
 

In 2006, the International Astronomical Union (IAU) declared that Pluto was no longer considered a planet but, instead, a dwarf planet. After Pluto was discovered in 1930, debate continued about whether it was a planet or maybe simply a small icy body lying beyond Neptune in an area that became known as the Kuiper Belt. In 1992, the first member of this area was identified. More Kuiper Belt Objects (KBOs) were discovered, including Quaoar (2002), Sedna (2003), and Eris (2005), which had roughly the same mass as Pluto.
These discoveries pushed the IAU to consider during their 2006 General Assembly in Prague what defined a planet. They produced a three-part definition. A planet should orbit around the sun. In addition, they declared that a planet has "sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape." The third part of the definition was that a planet has to "clear the neighborhood around its orbit." This means that it has to be dominant in terms of gravitation and have thrown other large objects out of its orbit. While Pluto met the first two criteria, it did not meet the last one, as there were other KBOs in the neighborhood of its orbit. Therefore, it was deemed not a planet.