Supplemental oxygen is both a physiological necessity and a regulatory requirement. The ATP must know the 14 CFR 91.211 crew/passenger thresholds, the differences between oxygen systems, and the special rules for pressurized aircraft.
At high altitude additional 91.211 rules apply. Above FL250 at least a 10-minute supply of supplemental oxygen for each occupant must be available for emergency descent in case of pressurization loss. Above FL350, one pilot at the controls must wear and use an oxygen mask continuously unless the aircraft is below FL410, has quick-donning masks, and two pilots are at the controls — in which case the mask may be off. If one pilot leaves the controls above FL350, the remaining pilot must don the mask. (Part 121/135 carry parallel, sometimes stricter, requirements.)
Aviator's breathing oxygen must be dry to prevent valve icing — never substitute medical or industrial oxygen. Keep oil and grease away from oxygen fittings (fire/explosion hazard), and know the difference between gaseous bottled oxygen and chemical oxygen generators (passenger drop-down masks), which produce oxygen by exothermic reaction and cannot be shut off once initiated.