There is a general misconception for most people when it comes to how to stabilize the core during movement and exercise. Many people believe that "sucking in" or "vacuuming" the stomach will turn on the core stability muscles and provide the support needed to lift objects. Others believe that holding one's breath or "bearing down" creates pressure in the core that provides stability. While both camps have SOME of it right, neither has it perfect. The IDEAL way to stabilize our core during exercise and movement doesn't start with abdominal muscle contraction or holding our breath; it starts with a big ole' "belly breath."
Diaphragmatic breathing is defined simply as the contraction of the diaphragm muscle downwards into the abdomen to allow the lungs to expand downward and outward while taking a breath in. As the diaphragm drops down, it compresses the organs, fluid, and other contents of the abdomen. The compression of these will cause the pressure inside the abdomen to rise. This is what we call creating intra-abdominal pressure. This increase in pressure presses into the spine and the pelvic joints and provides our natural core stability! "Bearing down" will create SOME intra-abdominal pressure, but since there is no diaphragm contraction because we are holding our breath, the pressure increase is limited; plus holding your breath during exercise or lifting has other consequences as well...
Chest breathing or paradoxical breathing is the opposite. The diaphragm does not contract on inspiration and we use the chest, neck, and rib muscles to lift the ribs up to allow the lungs to expand. What we lose is the compression of the abdominal contents so no pressure builds. In fact, the lengthening of the abdomen without the diaphragm contracting causes the abdomen to LOSE pressure. We compensate for that lack of intra-abdominal pressure with muscle contraction of the lower back, hip flexors, and ab muscles which can lead to muscle strains or tears or potential spinal disc or joint injuries.