In comparison to other games--Mario and Zelda, for example (and for something even more violent, we could look at games such as Call of Duty and Assassin's Creed, most of which are rated mature, but kids still do play)--Pokémon doesn't have much of negative effect, to be exact.
When battling, most of it is animation--we only see Pokémon throwing water, flame, thunder, and other things of the like towards each other, to prove who is worthy and whatnot, and become victor. They do get damaged, yes, but I don't believe these damage cause long-term harm to their body in any possible way. They're here just so they could knock Pokémon out temporarily.
Plus, having matches with Pokémon does more good than anything, as you're training them and making them stronger than they have been. Might not be a wise statement to base an argument on, thinking about it, but it's still there!