Well, it’s not really clear what practical value the exercise has, and I don’t usually engage in pointless grammar debates, but I would tend to disagree with your teacher. Let’s take a look at these two sentences: “All of the food is delicious.” “All of the people are eating it.” As you can see, the verb agrees with the real subject (singular “food” or plural “people”), not with the word “all.” The same holds true with “some,” “any,” “lots of,” “a lot of.” “Some people are eating.” “Some food is good.” “The man ate a lot of food” — the direct object is “food” — there is no “lot.” In my opinion, the phrase “all of” in your example is actually a partitive construction used simply to modify (quantify) the word “food.” Take this other example “The large man ate some (of his) food” = “The large man ate some food of his own.” “Food” is the direct object. I’d be curious as to what your teacher’s point was supposed to be.

Ate what? - "its food"