Did John F. Kennedy overthrow Castro?

Fidel Castro was ruler of Cuba when Kennedy became President, was still ruler during the entire Kennedy Presidency, and remained ruler long after Kennedy died.

Deliberately deceived by the CIA into thinking it would work, Kennedy authorized an invasion of anti-Castro rebels into Cuba. It was a complete and total failure, as the CIA knew it would be, but Kennedy did not follow this up with explicit US Military support.

In other Words, Kennedy WANTED Castro to be overthrown, but realized it could not be done without major repercussions.