most likely Itachi learnt the basics from his family but he was a ninja so that means he did have a ninja teacher.
although it might not be important at all, he could have had anyone as his teacher.
We know its not Kakashi or Orochimaru because Kakashi only ever passed Naruto,Sasuke and Sakura - we know its not Orochimaru because the only genin he ever took in was Anko.