In the beginning I don't talk much with new students about breath, although it is mentioned. They have much more to concentrate on.
Later, when they are becoming more proficient in tchnique and form, then breathing is concentrated on more.
In the end, they instictively know when to inhale and exhale.
Breath is so important in technique, but I feel that it is more towards the rhythm. The great breath to generate greater power is a must to know, but with correct timing, distance and balance, it is not needed.
Also, it is important where that breath comes from. Like in singing, it should come from low down ("from the stomache") not high up ("from the throat"). That's what gives the opera singer the power in his voice, and the Aikidoka power in his technique!