"I think he doesn't like it" is grammatically correct.
"I don't think he likes it" grammatically means "there is nothing to make me believe that he likes it" but is used idiomatically to mean "I think he doesn't like it".
Either phrase is completely acceptable, and would normally be taken to mean the same thing. Your English teacher is teaching you to pass English exams, and some marks in language tests are normally award for using idiomatic phrases and sounding "natural". Hence, within that context, I don't think your teacher's statement of never to use "I think...not..." was fine. However, in the real world, you can use either and there is no problem.