Fruits and vegetables aren't opposite things. Fruit is a term of art in botany, but it's lay usage is fairly close to that. The word vegetable can be fairly broad to include almost any edible part of a plant. This is why I'm a vegetarian and not a vegetarian and fruitarian.
Culinary vegetable is often used as a "soft opposite" of fruit because they often require different preparations and uses.
The interesting thing about "begs the question" is that it's a matter of who is doing the begging (asking). Classically your answer is asking for your premise, so you're sort of working backwards and likely circularly. In modern usage, the answer is asking for more research.
Sometimes people use it to mean dodging a question, which I'm not quite sure why and would consider wrong usage.
See also 'fruit', and whether or not tomatoes are displayed in the vegetable aisle.