When and why is the plural used?
We often use the plural in french to express a generality (Il n'aime pas les carottes, les tomates, les légumes...) But also les brocolis is the common way to translate broccoli in french. We use the plural.
Why not "de brocolis"? I thought negatives were followed by "de"?
I also wrote "de brocolis". I don't understand why it is wrong. Since "brocolis" is the direct object of "aimer", I thought this was exactly the situation when the "de" rule applies.
Why les and not des?
An excellent question !
Because when expressing a preference, you always use «les» . Kids don't dislike some broccoli («des brocolis»), they dislike all of them («les brocolis»).
On pourrait aussi bien dire dans un contexte général : "n'aiment pas le brocoli, l'oignon, le pain, le beurre, le fromage, le sucre, le lait, etc...