Breathing to both sides is extremely important, especially for training, and when young. You need to try and break the habit a soon as possible, even if you are an older swimmer. Breathing to both sides helps keep your stroke balanced. If you only breathe to one side it will make your stroke lopsided, and cause one side of your body to be stronger than the other, which can increase the risk for injury.

A lopsided stroke is also not as efficient. It is especially important to be able to breath to both sides during workouts. By training your body every day to alternate breathe, it will train your stroke to be balanced, so that down the road as you get older, you will be able to breath to your better side in a race without sacrificing any efficiency in your already balanced stroke. In other words, alternate breathing, especially when young, is important to help develop your stroke, so that when you get older you can revert back and still swim fast.

If you are not a young swimmer, I would still suggest training yourself to alternate breath in practice, and at meets for long distance races. Then as you get used to it you can switch back for your races. If you are a non-competing masters swimmer, I would still suggest alternate breathing, because it will ultimately help your stroke.

Alternate breathing is also a good way to train for breath control, and to help add rhythm to your stroke during long sets or races. Breathing every 3 or 5 strokes for a long set will help you much more aerobically than breathing every 2 strokes will. Even though it doesn't seem like it will make that much of a difference, it does.