@ucbalumnus you’re wrong. “If and only if” means that the prerequisite claim is the only claim that makes the primary claim possible to be true.
B can occur if and only if A occurs, but that doesn’t mean that because A occurred B occurred.
A = driving a car B = car crash.
B can only occur if and only if A occurs – you can’t be in a car crash if you aren’t driving a car.
But just because A occurred doesn’t mean B occurred.