Itzik was born in Jerusalem. Her parents were Iraqi Jews who had immigrated to Israel. Her family was poor; her father was an alcoholic and at times her mother had to steal food for the family to survive. She attended a religious high school, and afterwards, avoided conscription to the Israel Defense Forces by declaring herself religious. She then attended a teacher training course, and went on to obtain a BA in Literature and History from the Hebrew University of Jerusalem and a BA in Law from IDC Herzliya. She worked as a teacher, during which she headed the teacher's union in Jerusalem, worked as a deputy to Jerusalem mayor Teddy Kollek, and served as a member of the executive committee of the Israel Broadcasting Authority.