All trainers must be at least 10 to train Pokemon. If a child under 10 "owns" a Pokemon, it is only permitted if it is registered as a "family pet". They, however, are permitted to accompany older trainers on their journeys, but they may not participate in battles, the league, or any other form of Pokemon Contest.
Who cares what age kids playing the game are. Everyone in this world is going to summon Satan one day or another, let's go ahead and start them off early.