Well, it actually seems like a bad influence. Lol. xD
It seems as if the biggest lesson is to love the Pokemon you catch, according to the anime anyway.
The reason Satoshi Tajiri made this game was to let other children do what he did in his childhood - collect creatures. (bugs to be exact) Not many people could do it after his childhood, and so he felt sympathy and after six years of development Pocket Monsters was born. :3
So... really the biggest lesson is to love Pokemon over battling with them, but otherwise, the biggest lesson is to beat the stuffing out of other trainer's Pokemon! :D
Hope I helped.
Source: My wonderful, pink, plump brain.