Why do people practice Taiji quan so slowly?

Training slowly has several effects, for one it allows you to improve your stances and positions through self analysis. Having more efficient postures and eliminating gross wasted movements is one of the major benefits of taiji quan practice. If you do it fast you don't have time to analyze, even in Fast form styles you do it slowly in the beginning. Also Taiji practice is one way to bring a practitioner to a meditative state. Moving fast boosts the heart rate, hastens your breath, constricts the muscles and blood vessels cutting blood flow to the brain and pumping more blood into the muscles. These physiological changes make it quite hard to remain in a meditative state. Taiji quan is also a form designed to train you to keep your heart rate even and blood flow balanced even though you are in a stressful situation, such as combat. Training slowly keeps you in stressful stances for longer periods of time thereby increasing your strength in fighting postures much faster than training at fighting speed would. Slow training at first can be very stressful, you may even find your legs shaking, this is because your body takes time to adjust to new physical stimuli. One other point in taiji that many people are concerned about is breathing control, when you move slowly you are able to control your breathing more than if you were at a sprinting speed.