They protest pokemon because despite looking fairly innocent on the surface it's essentially about the enslavement of animals and the subsequent forcing of said animals into brutal and lethal fights. It's essentially a game about c0k fighting. Not saying I agree with PETA just saying it's not as inane as it first seems. Although I will say that anyone who is misguided enough to think that video games will automatically cause people to mimick crimes but then decides to fight a crusade against pokemon (rather than GTA for example) is somewhat lacking morally. They decide that pokemon is the worst offender because aparently c0k fighting is worse than killing hookers.
Pokemon also teaches the bond between a trainer and his pokemon (or an owner and their pet) and that all Pokemon should be cared for properly. If abused, people will try to stop Pokemon abusers and that is shown in the games and many of the movies. Pokemon fight but never to the death and they only will if they like their trainer. Even if a Pokemon is caught, it is not garanteed they will do what their trainer says (also shown many times in the games/anime) Pokemon also teaches lessons because of course, it's a kid game.