Why is more oxygen required at higher altitudes?
This question is best answered on https://biology.stackexchange.com, but in short it is the partial pressure that counts. This is (pressure in atmospheres) * (percentage).
At 0.5 atm (18 kfeet) you need twice the amount of oxygen in the air (aka 40%) for it to have the same effect on you. Above 38.5 kfeet the pressure is 0.2 atm, so even 100% oxygen will only provide 20% partial pressure of oxygen, which is the same as normal air at sea level