I agree with peachey. We use 'what' when there is an indefinite (and often large) number of possible answers. We use 'which' when there is a definite (and often small) number of possible answers. 'What' relates to the indefinite word 'a', and 'which' to the definite word 'the'. What sport...? (a sport) (Tennis, or golf, or football, or...) Which way...? (one of the ways) (Right or left?) 'Which came first, the chicken or the egg?' 'There are lots of books here. Which do you want?' 'Which' can come before one/ones or before an of-phrase. 'Which of these postcards shall we send to Angela?' 'What book are you reading?' In some contexts either word is possible. 'What parts/Which parts of France have you visited?' 'What size/Which size do you take?'

"Which" means there are options. "What" is asking for a specific thing. So "which is your favourite food?" is asking your preference out of the many food possibilities. "What is your favourite food?" is simply asking for a specific answer - not so interested in the options. Really, I don't see a problem in using either one in that context. Just remember the "options" element to using "which".

Well, in traditional English, your teacher possibly has the reason, because for instance, in French, such kind of questions would only allow the usage of "which": Which is your favourite food? = Quel est ta/votre nourriture favorite/préférée? In the above example, the corresponding French interrogative adverb, "que", would not well fit into the context. However, as respondent Peachey stated, when there is a choice of selections, then the interrogative adverb "which" is required, while if the question poser only cares about a particular answer, then the interrogative adverb "what" is preferred. Additionally, respondent Learner has provided a number of good examples for references. Take care, and good weekend. / 祝 週末愉快。