Because in the Pokemon world, everything is in a state of relative anarchy so proper schooling cannot be officially arranged. Seriously. Have you ever seen a trace of any government beyond the occasional Mayor? The only reason the economy is stable is the population's dogged obsession with spending money on Pokemon-related goods.
Think about it this way; the only schools around are Pokémon schools, right? Well, in the world of Pokémon, being good at Pokémon battles can get you a lot of money. So kids below age ten are sent to (Pokémon) school, and when they're ten they're kicked out of their house by their parents (apparently by the order of their TV) and go out into the world to earn money. (Just ignore the giant holes in that theory and it's completely plausible!)
Seriously though, I think it's covered by a concept called "(willing) suspension of disbelief". In short it means that if something is interesting, with some truth or realism, you can get away with a lot of stupid things. At least that's the best way I can explain it; the curious might want to read some into it on wikipedia or TVtropes.