This is a question that is asked a lot. In reality, it does not matter whether you breathe to the right or the left. However, if a swimmer always breathes to one side he/she typically will develop an asymmetry in their stroke. This may be pulling harder with one arm than the other, having more body roll to one side, etc…

The most efficient swimming comes when an athlete's stroke IS symmetrical. One of the best ways to do this is to focus on alternate breathing, or breathing to both sides in practice. In breathing to both sides in practice, you set up good habits and should develop a symmetric stroke. Then in the race, it should not matter if you breathe only to one side. The symmetrical stroke that you developed in practice should still be there for the competition.