When he reaches the top of Mount Everest, why is Krakauer in a hurry to start

back down?

Oxygen supply become alarmingly low. This is why Krakauer is in a hurry to start back down when he reaches the top of Mount Everest.

Explanation:

"Into Thin Air" by "Jon Krakauer" is story about the author who climbed Mt. Everest. He saw the amazing view of Tibet below him, but he was not able to appreciate it. He was feeling weak and cold. Jon was constantly coughing, and all this was the result of extremely low levels of oxygen due to which his brain was also not working properly.

That's why he asked "Andy Harris" to conserve the oxygen, but Harris opened the flow of the oxygen. Though he felt a lot better after the oxygen supply, but soon he realized that he would have to go down without oxygen to reach South Summit where another oxygen tank was kept.