"Aid" is a bit of an understatement considering that Castro was fighting against the US-and mafia-backed dictator (Fulgencio Batista). The withdrawal of American support to Batista happened because the corruption and violence had reached unsustainable levels even for an anti-communist.
People make this argument - but it’s consistent through history with moderates as well as non-moderate government. Withdrawing support is always seen as weakness an established state and leads radicals to overthrow governments. Germany 1931(bankers withdrew funds), Afghanistan, Cuba, Vietnam.