Every swimmer should breathe every 3rd stroke during freestyle training. Many are reluctant to change. Allow me to state my case:
Exhibit A: Breathing bilaterally keeps your stroke even. Ever seen a swimmer who "limps" as they swim? Was he breathing every 3? Exactly.
Exhibit B: Breathing every 3 helps avoid neck and shoulder tightness. Swimmers who breathe only to one side try this: Turn your head to the right. Turn your head to the left. Is your flexibility equal in both directions? Most likely you can turn your head further to your breathing side.
Exhibit C: Head position determines body position. We breathe with our heads. In my observation, 99% of freestylers could improve their breathing mechanics. Thus with better breathing mechanics, almost every swimmer can improve her body position, reducing drag.
Exhibit D: Every action has an equal and opposite reaction. To pick your head up or to pull your head to the side to side to breathe, you must support that position. Thus, unless your breathing mechanics are perfect, you are exerting energy and effort to support that imbalance. This is energy that could be used to propel you forward.
Exhibit E: "I get less oxygen when I breathe every 3rd stroke," say the every-stroke-breathers. Changing a habit is not easy. Learning a new skill takes time. At first, you will get less oxygen when you breathe every 3. As you develop your bilateral habit, you will learn to relax and breathe deeper. Soon you will be able to take in nearly as much oxygen as before.
Exhibit F: With imperfect breathing mechanics, the equal and opposite reactions can often cause stroke irregularities that can cause injury, most often to the shoulders. Who would have thought that simply breathing could injure you?
The floor is open for cross-examination.