Curly hair is less hydrated than straight hair, and it's this lack of hydration that causes frizz, making hair look dull (read: no shine). Not enough hydration also triggers brittle hair, which leads to more split ends. All of this is caused by your curl pattern, not a natural inclination that you have for drier hair. The oils produced on your scalp — a.k.a. sebum — are what hydrate hair, adding shine, decreasing frizz, and giving it strength.
For those with straight hair, those oils slip down the shaft rather easily — brushes help, too, pulling oils from the scalp down and distributing them throughout the hair. Since brushes are taboo in the curly hair community and it is more difficult for oils to slide down a spiral or coil, curly hair textures are drier than straight versions.