Myth – “Breath Control is the critical component of marksmanship fundamentals.”
Fact – Shot placement is determined where the barrel points, as indicated by the aligned sights, when the trigger is pressed.
It is common, especially in military circles, to believe that breath control and/or breathing has some mystical effect on shooting and will magically cause shots to go high or low.
Any movement, whether caused by breathing or any other factor, will show as motion in the sights. While the hold may wobble, the shot will always be where the aligned sights indicate when the trigger breaks (assuming a good zero and ignoring trajectory, of course.)
All breath control does is pause the shooter’s respiration while executing shot(s), thus helping to minimize movement. That's it! Pause breathing while pressing the trigger and breathe normally at any other time.
The problem is novice shooters often tend to hold too long, over-staring the sights, holding their breath until blue in the face, and probably inducing a flinch just to be rid of the chambered round. Breath control alone can't cause shots to go high or low. Even if it somehow could, the shooter can see that aiming error with the sights. This assumes the shooter can call shots and fire without flinching.
Breath Control does have one important contribution to improved marksmanship: If you're on a range and over hear “advice” such as “Watch your breathing” you can probably ignore anything that person says about marksmanship because he has just identified himself as someone who doesn't understand the subject.