There are two ways in which the body breathes. First is in the chest. (This is how we breathe in an exercise like Standing Deep Breathing.) Breathing in this way uses the intercostal muscles, which are made up of several sets of muscles that expand and shrink the ribcage and chest cavity. Using the intercostal muscles effectively requires that the abdominal muscles are relaxed. The second way in which the body breathes is known as “abdominal” or “belly” breathing. This breathing uses the diaphragm and the transverse abdominis. (This is how we breath in Kappalabhati.)
When we do Plank pose, we largely rely on the rectus abdominis, or six-pack muscle, to stay engaged. This engagement slightly pulls our ribs down and in, toward our pubic bone, which keeps our spine straight. Without this engagement, we would do something resembling a sway back. The rectus abdominis is however, intricately connected to the transverse abdominis which is not just a breathing muscle but, especially in a pose such as Plank, also a muscle of stability.
When breathing, it is next to impossible to inhale without the transverse abdominis relaxing, especially in abdominal breathing. However, this is also the case if you breath into the chest, since the abdominal muscles have to release for the ribs to lift. So, considering all of these muscular functions means that any inhale you take in Plank pose (especially a deep one), will cause the abdominal muscles to relax. Since the abdominal muscles are what support this position, breathing in this posture will actually destabilize the spine and release the structure of the posture.



