That's not actually true. If you research it, you'll find that most people's nostrils alternately dilate and contract (the tissues reduce/swell). Most of us breathe primarily through only one nostril at a time, and it switches approximately every half hour. This is entirely unconscious and we're generally not aware of it.
There is a little bit of airflow in the constricted nostril, but nowhere near comparable to the other. You can test this by covering up your nostrils individually and comparing how easy it is to breathe through them. Then wait a half hour and try it again. (Note that a minority of people do not have this.)
However, this is not something you can consciously control or override, any more than you can override contractions in your intestine.
There is a little bit of airflow in the constricted nostril, but nowhere near comparable to the other. You can test this by covering up your nostrils individually and comparing how easy it is to breathe through them. Then wait a half hour and try it again. (Note that a minority of people do not have this.)
However, this is not something you can consciously control or override, any more than you can override contractions in your intestine.