Fluttershy knows the Everfree Forest better than anypony else. And she knows that what's been happening is not natural.
Animals are being hunted for sport, brought down with precise strikes that leave only the smallest of holes. It's no animal. It's not magic. And that idea terrifies her.
So when Twilight Sparkle vanishes into the Everfree, Fluttershy takes it upon herself to find her, even if it means confronting whatever horror lurks within.