My educated guess is that "Shy" inherited the ability to intimidate animals (if not most ponies) from either her family life when she grew up in Cloudsdale. Going out on the proverbial limb, I speculate that Fluttershy and her mother were frequent victims of physical abuse by "Shy's" father, and Fluttershy learned to stand up to her abusive dad by developing The Stare to fend for herself and her mom.
On a different note, I'm also speculating that Fluttershy's brother (as announced at San Diego Comic-Con by Andrea Libman) possibly could actually be her half-brother, sharing the same mother but different fathers. After Fluttershy's parents divorced, "Shy's" mother married a new Pegasus pony and gave birth to Fluttershy's brother/half-brother. Fluttershy had a (somewhat) better relationship with her step-father (and half-brother) then she did with her real dad.
Nevertheless, a few years later, Fluttershy was old enough to move to Ponyville for the first time in her life so she could make a living caring for animals.