You don't have to be initiated to become a Witch.
In some forms of Wicca one needs to be initiated, but not in all forms. And Wicca and Witchcraft are different in any event.
However, I would also say that even if you have an ancestor who was a Witch, that does not make you a Witch. Think of it this way, say you had some ancestors who were great pianists. Despite that, if you never sat down at a piano, learned to play, and practiced regularly you'd never be a pianist yourself. Same with Witchcraft. You become a Witch by doing the work necessary to learn how to go about it.