Wow! Thanks for illustrating all of the things that are problematic about attitudes toward children today! You see, we are so concerned about protecting little Suzy Q's fragile little ego, that we forget what a little monster she could turn into when things don't go her way.
This kid thinks she just so gosh darn entitled that who cares what the adult says. . .she is going to do whatever the heck she wants (and destroy property in the progress and potential injure the horses and herself) because no one ever bothered to put a limit on this kid's world. Perhaps a trip to the proverbial woodshed would have done this girl a world of good!
Interestingly, my 11 y.o. nephew was listening to me rant about this earlier (before the OP indicated that the kid had damaged the fence) and said that the kid would probably do something mean in response. His mother asked him if he thought some of his friends would do that. He said yes. His mother then asked if he knew what she would do to him if she ever heard of him doing anything like that (a good, respectful kid who loves horses and would never even think of such a thing). He got a panicked look on his face and said that he didn't want to think too hard on that but he was pretty sure he wouldn't sit down for about a week -- which would be bad since he would be grounded with nothing else to do for that week and beyond! (Note: My sister is in no way abusive, but she has *gasp* spanked both her boys and they are about the happiest and most well adjusted and nice to be around kids I have ever met!).