Breathing is a necessary process so that humans stay alive. The cycle of respiration is that we inhale oxygen, the body converts it to energy, and we exhale carbon dioxide.
Now, for singing, we must not inhibit this natural cycle. Thus, no pushing air out and no holding air. We breathe in, the cords close for a split second as the body is converting oxygen to energy, and this is when we sing with carbon dioxide being exhaled and transformed into soundwaves.
As a singer, the breath has two functions:
As necessary as the breath is for singing, it is still secondary in that the correct adjustment of the vocal muscles (registration) must take place or energy will be wasted, as well as the moving air not shaped properly if the size of the glottal slit is too big or too small. For it is the vocal cords that act as a valve that let out how much air needs to go out requisite to pitch, volume, and vowel.
If the cords ain’t working right, then nothing we try to do with the breath will fix them. The breath will just leak out. Correct moving muscle determines the ability of the air to move correctly with usage of the breath being economical as a result.