Making a big sound is not primarily about pushing a faster stream of air over the vocal folds. It concerns maintaining a pressure from the lungs that relates to that of the cavities above the larynx. Under gentle and controlled pressure the folds can vibrate naturally and the mechanism works as a sympathetic whole.
Breathing is controlled by an involuntary muscle called the diaphragm. The singer has to learn to control the surrounding stomach muscles to create a steady constant pressure on the diaphragm while breathing out. Training these muscles allows the fine control of upward pressure from the lungs that is necessary for good singing. This is referred to by singers as developing support. (A side effect is that singers develop extremely strong stomach muscles.)
