Nopony knows why it happens. It's senseless, horrible, and cruel. Upon growing up, a few unlucky ponies develop animal features, like antlers, whiskers, scales, or even beaks. These hybrids, these fuzzies as they are known, are shunned like freaks and treated like beasts. The world would be better off without them, according to everypony else.
For the most part, Twilight would like to pretend that these sub-equines don't exist, but she can't ignore it when Fluttershy falls victim to the curse. This seismic event threatens to tear them apart. She feels like she has no choice but to sever ties and abandon her friend. Ponies have very good reasons for hating fuzzies, and Twilight knows those reasons by heart. It's the right thing to do... isn't it?
Regardless of what she thinks, there's no room for fuzzies in a civilized world, and that's not about to change any time soon. Only a fool would think otherwise.