These are a few of the most common causes of shooting left (for a RH shooter):
1. Holding the dominant eye to the left of the arrow, rather than directly over the arrow.
2. Torqueing the bow.
3. Torqueing the string.
4. Pushing the arrow. This happens when the drawing elbow is not all the way behind the arrow because the shooter didn't come all the way to full draw.
5. Creeping. When there is a loss of back tension just prior to release, but not severe enough to cause a pluck. This can cause a right or left miss. As a part of followthrough, hold back tension until after the arrow leaves the bow.
6. Peeking. When the head is raised as the arrow is released, whether to actually see the arrow in flight better, or perhaps as a reaction because the string or something has been hitting the nose or cheek. Keep the head still until after the arrow hits the target. This can cause a right or left miss.
7. Lack of concentration. It is important to be concentrating on the spot at the moment of release. Sometimes people concentrate on the spot until the arrow is aimed, and then their attention drifts at the moment of release. This can cause a right or left miss. As a part of followthrough, you should continue concentrating on the spot after the arrow is released.
8. Poorly tuned arrows.
9. Prematurely dropping the bow arm. As a part of followthrough, you should keep your bow arm up until the arrow hits the target.
10. Shooting on a side hill that slopes off to the left.
11. Changing from a bow cut past center to a bow not cut to center. If you want to do this, you have to allow time for your mind to adjust.
Edit: Almost forgot the most fundamental reason of all: upper body not in alignment. (Sorry, Terry!)