Why a US invasion of Cuba would not automatically break NATO

Would Britain walk out of NATO if the United States invaded Cuba?

Not necessarily; NATO members could decline to support an offensive war and pressure Washington diplomatically without leaving the alliance.

An American attack on Cuba would fall outside the defensive circumstances that activate NATO obligations. Britain and other members could refuse to participate without immediately abandoning the alliance. They would still have many diplomatic ways to impose costs or signal opposition to Washington. The larger danger would be a Soviet response that widened the crisis and created new problems for both NATO and the United States.