Our bodies need a lot more chemicals besides oxygen. Carbon dioxide being a very common one, this 'hangs' in the bottom of out lungs and it is crucial to have a proper oxygen/CD balance.
When we hyperventilate through stress or fear, our lungs have a shortage of carbon dioxide, not oxygen. That's why breathing in an paper bag works because we inhale the previously exhaled CD. Breathing fresh air deeply in those situation only makes matters worse.
Fish have different blood to mammals and use a lot less oxygen so they can utlilise the oxygen in the water.