Being a unicorn that can actually use spells beyond levitation is like picking a class in D&D, and not everyone gets a class.
Basically. Every unicorn specializes in something. A few unicorns, like Twilight, Starlight, and Sunset, won the metaphorical lottery and specialize in magic itself.
Things like light, telekinesis, and teleportation, theoretically any unicorn can do, but while the first two are easy and require only a modicum of power or skill, teleportation is a whole other beast. Twilight herself only mastered teleportation after becoming a young adult.
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