A) It's PETA. You expect logic from them?
B) PETA's stance is that the fighting in the game between Pokemon is a form of abuse
C) It's PETA.
On the one hand, they kind of have a point. On the other hand, these animals do not exist. They're 1's and 0's. Despite playing Pokemon (and having done so since Gen 1) I have a loving relationship with my cats, and have never done wrong by an animal. I still find stories of animal abuse despicable, with the worse cases causing me to feel physically ill. Pokemon has not desensitized me against animal abuse in the slightest.
And they use Ash as an example? Knowing what I know about the TV show, Ash would never let Pikachu be that hurt unless he were failing horribly at being himself or Pikachu basically forced him to let it happen.
Thanks to araveugnitsuga for my current Poke-atar.