First of all, it is only in astronomy that Pluto is no longer "a planet".
If you are not an astronomer and you want to call Pluto a planet, go right ahead.
Because of "definitions".
In science, precise definitions are needed in order to be able to give detailed (and precise) explanations for things.
Over 2000 years ago, the Greek philosophers used words like "aster" (star) for anything that was in the heavens (beyond the atmosphere -- they did not have the concept of "space" yet), and the word "meteor" for things that were in the atmosphere. That is why the study of what happens in the atmosphere is called "meteorology" and, in that science, things like clouds, snow, hail and so on are called "meteors".
In the "heavens", you had fixed stars and you had stars that moved (in a predictable way) among the fixed stars. The moving ones were called "aster planetes" (meaning "stars that move") and the Greeks knew of seven of them: Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn.
There were also unpredictable stars that looked as if they trailed a head of hair blowing in the wind. They called those "aster cometes" (stars with hair). The comets have nothing to do with our story... until the very end.
Back to the "planets". They moved among the fixed stars in a predictable way (once you knew how each one moved, you could predict where it would be years in the future). In 1610, when Galileo discovered "things" in orbit around Jupiter, he called them "planets" -- which was OK using the definition of planets that existed back then.
But after Newton finally proved that the Sun was at the centre of the system (around 1687), the definitions changed.
Planets were objects in orbit around the Sun. The Earth suddenly became a planet (not because the Earth had changed, but because the definition of planet had changed). Things in orbit around planets became known as "satellites" (although unofficially, many people continued to use the simile "moon", as in "the moons of Jupiter"). Our Moon lost its planet status and became a satellite of Earth.
The Sun also lost its planet status and got promoted to "star".
Fast forward to the 19th century (the 1800s). Early in the century, 4 planets were discovered between Mars and Jupiter (Ceres, Vesta, Juno, Pallas). They were in orbit around the Sun, therefore they were planets. However, with the arrival of better telescopes around 1850, these things were being discovered by the dozen. By the early 1860s, it was clear that they were "special". It was clear that these objects were not like the other "real" planets. They were so small that, even when cranking up the magnification, they still looked like pinpoints of light, just like the stars: each one was "asteroid" (meaning = "looks like a star").
A new category was created, called "minor planets" and these new objects lost their "planet" status and were included in this new category.
Fast forward again to the early 20th century (early 1900s). Pluto was discovered during an international program searching for a planet. Also, once its distance was calculated, it appeared so bright - for that distance - that everyone thought it must be huge (up to 4 times bigger than Earth). Therefore, it was called a planet.
In the early 2000s, using better telescopes and photographic equipment, other similar objects are being discovered. It is a repeat of what happened in the 1800s. Also, in the meantime, every time astronomers tried to determine Pluto's real size, it always seemed smaller than we thought. Today, we know that it is only 1/6 the mass of our Moon.
Same problem as in the 1800s, therefore, same solution: create a new category (dwarf planets) and list Pluto as the first object of this new category.
As a bonus, as we are trying to understand how planets formed around the Sun (around 4.5 billion years ago) we find that the gas giants formed first (Jupiter, Saturn, Uranus and Neptune), followed very soon after by the "terrestrial" rocky planets (Mercury, Venus, Earth, Mars).
It is only after the Sun's internal "furnace" turned on that the Sun's new light pushed out all the small stuff (gas, dust, etc.) out into what we now call the Kuiper belt, and that is where (and when) Pluto formed.
Pluto formed in a way that is very different than the way the "real" planets formed. The way Pluto formed is a lot closer to how comets formed. The reason it looked so bright is that it is mostly a ball of ice.