Pluto is not a planet - the only reason why people thought it was a planet was because of historical reasons:
You see, when Pluto was discovered, scientists had gotten into the habit of trying to predict planets. They predicted Neptune and Uranus, and lo and behold there they were. Actually, it was pure luck that their predictions co-incided with reality. They had no real reason to believe that these planets were there, but they got lucky.
So they started to predict the existence of a ninth planet. They had almost no reason to believe there would be a ninth planet, but by this time a lot of careers were riding on its prediction and they were desperately looking for any hint of it.
Then, luckily, someone spotted something a bit bright in the sky. It was very faint, but it was.... just.... barely.... visible. Not only that, it followed an orbit and maintained its size and shape. Instantly they lept up and down and said they had discovered the "ninth" planet.
This was in early days of proper astronomy, so they didn't know how wrong they were.
Truth is, there are plenty of larger objects that follow orbits around the sun, some of them closer to the sun than pluto. Pluto was only spotted first because it is very bright (being largely composed of ice).
If you're going to call pluto a planet, well, hold on to your hats because you're going to have to call a lot of other "objects" planets. You could end up with a solar system with as many as 14 "planets".
Now some would say, well, Pluto has a moon, so it must be a planet. Well, yes, there is another object orbiting pluto, called Charon. But Charon and Pluto actually orbit each other - they circle each other and it is not clear which is orbiting which. And besides, Mercury doesn't have a moon yet it is a planet.
For me, a planet is anything larger than the Earth's moon, that compresses itself into a spherical shape by its own gravity. Of course, other people would have their own definitions. But Pluto is clearly not a planet. The only reason why it was ever classified as such is due to some silly predictions, bad technology and primitive times.