During the Golden Age of Piracy (1650-1730), pirates were primarily focused on plunder and survival. They operated their ships in small, loosely organized crews, often on the run from the law. While they might capture exotic animals during raids or voyages, keeping them as pets would have added logistical challenges.
Parrots and monkeys require specialized diets, housing, and care. These animals can also be loud, making them impractical companions for pirates who needed to avoid detection while hiding or attacking.
Pirates were more likely to keep practical animals such as dogs for protection, cats to keep rodents under control on their ships, and farm animals for food.
The romantic notion of pirates with parrots and monkeys is likely rooted in the desire to portray pirates as exotic, adventurous, and slightly comical characters in literature, movies, and popular imagination.