The reason I started the discussion is because I think examples like "fruit" where the common usage of the word deviates from any strict definition can help us to understand language and language acquisition better.

I suggest reading up on Eleanor Rosch's prototype theory, it explains the whole categorisation thing very clearly. The basic theory is that our categories aren't Aristotelian classes, but are fuzzy, and formed from seeing exemplars of a class and extracting the most common features. It's a well-understood property of cognition and has plenty of experimental backing.

In the case of cucumbers, I'd say it fails the 'fruit' test because it lacks almost all the features I associate with fruit: it's not red/yellow, it's not sweet, I don't eat it for a snack or dessert, and it doesn't have obvious seeds or pits inside. Therefore I would look at you very oddly if you told me that it was.