A few points:

Most if not all of the pyro kills are going to be by surprise. Of these, some come from killing a lot of people in a bottleneck like Goldrush. The non-surprise kills come from ubersor finishing people off.

You can kill any class as long as you catch them off guard. Jump behind a heavy and let the flamethrower go, most of the times you'll win. Same goes for a soldier and a demoman.

Pyro vs Pyro: Let him chase you and run backwards, your flames travel towards the other person and they just run towards their own. Watch if they change to shotgun and change also. They probably have little HP and will die in a few shots.

I personally like to get my kills in bottleneck areas of a map and catching others by surprise, like jumping from above or anticipating them coming from a corner.