Headcannon time
The Cullens aren't vampires, but they're actually fae. They go with the whole vampire thing because it's what Bella stated and allowed them to still keep their true nature hidden. Being fae explains the variety of abilities, the secrecy, the ability to sparkle and mesmerize humans, their smell, and can even explain the consumption of blood according to some lore about the Unseelie Fae.
The volturi are the leaders of the unseelie fae court and they all use the ruse of vampires because it's what humans automatically assume. Very similar to the wolves being mistaken for werewolves instead of shifters, except the Cullens and other vampires know their true nature and choose to obscure it as a form of secrecy.
Update: this also explains why we never see iron of any kind in the Cullens home. No fancy wrought iron fences or banisters or anything like that. And why Edward really hated Bella's truck..it was old and primarily composed of iron or materials containing iron. So yeah..I think they're Fae
