Final answer:
The US wanted to overthrow Fidel Castro when he took control of Cuba due to concerns about rival nations gaining control, Castro's policies harmful to US business interests, and his alliance with the Soviet Union.
Step-by-step explanation:
The United States had multiple reasons for wanting to overthrow Fidel Castro when he took control of Cuba.
Firstly, preventing rival nations, especially Communist ones like the Soviet Union, from gaining control of Cuba had been a longstanding policy of the US due to its proximity to the US mainland.
Secondly, Castro's actions and policies, such as centralizing the economy and restricting religious and media freedoms, were seen as harmful to US business interests.
Thirdly, Castro's alliance with the Soviet Union and the threat it posed to US national security further motivated the US to seek his overthrow.