Why is the pirate stereotype the way it is?

It's all based on the book 'Treasure Island' by Robert Louis Stevenson (published 1883).

2 movie versions, in 1934 and 1950, combined with the book, depicted pirates in the way you describe, and the image has stuck in the popular imagination ever since - reinforced by later screen depictions of pirates.

I'd chalk it up to literature. If you think about it, while hooks and peg legs were actual pirate prosthetics the public imagination of what a pirate looked like has been largely shaped by literature, which has been reinforced by movies featuring some of these literary pirates.. Treasure Island, for instance, gave us one of the quintessential literary pirates, Long John Silver. A man who has lost a leg so he walks with a crutch and has a parrot. The image was a major influence on how we think of irates today.

Colonial powers, particularly Britain, Holland and Spain, depended on freedom of the seas to maintain their colonial power base. Pirates of that time were a threat to that freedom, and can be compared to present day international terrorists. Just as we stereotype and demonize a "terrorist" of to-day, the pirates were stereotyped for the same reason. It gives the government the leverage to spend the kind of money needed to hunt them down.

I also agree with the above answerers. Hollywood and literature has had some influence.

In American and British popular culture, the modern pirate stereotype owes its tradition mostly to depictions of Captain Hook and his crew in theatrical and film versions of Peter Pan, Robert Newton's portrayal of Long John Silver in the film Treasure Island, and various adaptations of Sinbad the Sailor.