we can hold our breath under our control so how can it be involountary action?

Breathing is both involuntary as well as voluntary. We keep on breathing all the time without even realising it, this shows that breathing is an involuntary action. However breathing can also be controlled voluntarily. For example - A self-initiated change in breathing before a vigorous exertion or effort. Speaking, singing and playing some instruments (e.g. flute, saxophone, trumpet, etc.) are good examples of the behavioral control of breathing and are short-lived interventions.

The differentiation between voluntary and automatic (metabolic) breathing is that automatic breathing requires no attention to maintain, whereas voluntary breathing involves a given amount of focus.