Typically, the breathing pattern for a clean, swing, or snatch has the inhale timed with the hike or eccentric portion of the movement and the hard exhale timed with the hip extension. This coordinates the breathing and intra-abdominal pressure for the kettlebell ballistics.

But for the Military Press exhaling during the clean will mean you need to reset the breath before you can begin the press. After finishing the Clean while loaded by the kettlebell, inhaling can be challenging and lead to tension loss for the press. Instead, inhaling through the Clean into the loaded rack position sets you up for a strong press without losing tension, trying to reset the breath. The exhale in the top third of the press amps the strength again for a strong lockout.

The negative of the press is enhanced by inhaling during the active pull-down of the kettlebell to the rack position. It is again setting up a strong press.