Like everyone else, I find this lesson very confusing, and I think it is because it's using a very poor example of when to use articles. I believe the translation is incorrect.
Je n'aime ni le fromage ni le lait.
I like neither cheese nor milk.
If this example is talking about specific cheese and specific milk, then the English translation should be, "I like neither the cheese nor the milk." But that is not what you have here. The translation you give is general, not specific. It really makes the whole lesson contradictory and confusing.