Basic Biology question - why can I breathe through only my nose even when my mouth is open?

As I understand basic human anatomy (and granted, most of what I know comes from my 11th grade Biology class), the act of breathing has nothing to do with the nose or mouth. Instead, when you consciouslessly tell yourself to breathe, you are in fact flexing your diaphragm muscle. This has the effect of either bringing air into the body or expelling it out.

Under that system though, it would seem that on an inhale, the air would travel from the outside world into the lungs through whatever orifices are available. That is, if the mouth is open, air should go in via both mouth and nose. Similarly for exhaling, air should exit via both.

Yet that’s clearly not what happens in real life. You can choose whether to breath through your nose or your mouth, even when both are open and unplugged. What is the mechanism that determines that? Is there a “switchback” somewhere near where the two passages combine? If so, what is it called?

Thanks!