Hansel & Gretel is about parents deliberately leaving their kids in the woods, and then a witch imprisons them, which is eventually resolved by throwing her into the fire.
Little Red Riding Hood is about a wolf that eats a little girl's grandmother.
Snow White only gets to meet the seven dwarfs because her mother-in-law has decided to have her killed.
There are many more examples, which is to say - "our" "own" culture's children stories are not necessarily less violent.
It's not much different from the Bible, the stories are there to push your fear buttons in order to get you to comply. For children: if you don't behave your parents will abandon you in the woods to deal with the wild animals, for adults: if you don't behave you will burn forever in hell.
While I grew up on and love Grimm's fairytales, I am not sure if they are a good example of "our" culture. They have been edited ever since they were trusted to paper to reflect their editors' views on what "our" culture should be. The stern lutheran Grimm brothers themselves actually tuned up the violence in subsequent editions and stripped out the sex and incest (e.g. the devil in the Girl With No Hands was originally her father: try reading that version to your five year old daughter). And later Disney further defanged the stories by removing most of the violence as well.
The difference is - the fairy tales are presented as fiction. The stories adults tell you to make you behave are presented as reality.
It's the difference between reading your kids Smurfs and Bible (if you're Christian). I remember understanding the difference pretty early (and wondering why Bible seems like Smurfs but is treated differently).
Hansel & Gretel is about parents deliberately leaving their kids in the woods, and then a witch imprisons them, which is eventually resolved by throwing her into the fire.
Little Red Riding Hood is about a wolf that eats a little girl's grandmother.
Snow White only gets to meet the seven dwarfs because her mother-in-law has decided to have her killed.
There are many more examples, which is to say - "our" "own" culture's children stories are not necessarily less violent.