Because you rely more on your diaphragm. In order to whisper you need to maintain a continuous, reduced air flow. You need to control your diaphragm so that the air doesn't leave your lungs as strongly as when you're talking. Working on diaphragmatic breathing is a huge aspect of many therapies for stuttering. Not only that, whispering increases the length of time needed to articulate sounds, and often you end up exaggerating the movements so that the person you're whispering to can understand what you're trying to say. This slowed exaggerated articulation is another big point in therapies for stuttering.