Question

Why might Castro have sought to nationalize American business in Cuba

Answer 1

Cuts the power of American businesses--American businesses have used their economic power to leverage political power in many countries including Cuba.

By nationalizing American businesses (government control of the business), the government is able to manage the economic power of those businesses. Americans have used their economic control to leverage political power in places like Hawaii, Latin America, Mexico, and in Cuba. This would explain why Castro would want to take control of American businesses.