How does a boll weevil destroy the cotton plant?

It eats the cotton.

They eat the buds off the cotton plants. The boll weevil does not destroy the cotton plant directly, it destroys the boll wherein grows the cotton and its seeds.

The boll weevil has this big snout and it uses it to bite the top of the cotton plant. Then it licks out the cotton until it has no more cotton inside the ball. The boll weevil larvae and pupal do...

it tears the cotton off and eats it

Yes they do and they'll destroy grain, fruit, vegetables, and Cigarette's.