Is breathing completely involuntary

Yes ... because it can't be controlled by us ... it is controlled by our brain ... if it were to be controlled by us then we would end up dead if we fall asleep ...

Also, it is a known fact that nobody can't kill themselves by holding their breathe

Kind of, it's a natural reaction but your concience can suppress it.

You can, in theory, hold your breath long enough to pass out, but once you pass out you will naturally begin breathing again.