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There's even a counter specifically for chopsticks. Even though they're cylindrical objects, chopsticks are their own semantic category within cylinder-like things
Also birds and bunnies are a distinct category within animals, so while there's an animal counter, birds and bunnies have their own specific counter. Bunnies are a type of bird 
Sanbon biru anegaishimasu!
For beer it's actually sanhai (counter for drinks)
Similar with Chinese, bird, fish, land animal, even plants...
Or birds are a type of bunnies
Personally, the cases that I find more interesting are those where the native speaker chose the wrong classifier for the counted object. It looks like a demonstration of prototype theory
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