Altitude sickness has been studied since WWII when bombers were not pressurized, but did have oxygen masks. Still, there is no conclusive evidence as to why some people get it and others don’t. Fitness is not the key, as some marathoners suffer from it and some less fit people don’t. Slow acclimation to climbing high helps, but still some people have it.
I’m lucky not to ever have any sysmptoms other than mild headaches. Most people at altitude above 12,000 feet find their appetite gone, and food all tastes like cardboard.
I have climbed all my life, and in my mid-70s did four 14ers in California, including Mt Whitney at 14,500 feet. I had three friends do the three-day hike, and at camp around 12,000 ft, two got so sick they had to go back down the next morning. The 24-year old guy and I went to the summit and back down the next day, with no ill effects. We were humping 40-lb backpacks too.
There are two serious forms of altitude sickness, HAPE and HACE (High Altitude Pulmonary Edema and High Altitude Cerebral Edema), either of which can kill you. The only cure is to get the hell down to lower altitude as quickly as possible.
In my experience climbing many U.S. mountains, those prone to the problem usually begin to experience it between 10,000 to 12,000 feet. Sometimes it is mild enough to continue climbing, other times I have seen pretty fit people laying the ground, gasping like a fish out of water. It can also cause dizziness, nausea, disorientation, etc. If a severe headache or fits of coughing start, go to lower altitude immediately.
Climbing mountains like Mt Everest requires a series of going up to a higher camp for a day or so, back down to the lower camp, then back up a higher one, etc over a week or so until the last camp before the summit is reached. Then, if they are lucky in weather, they may or may not make the summit, but by then it is important to get back down as far as possible as quickly as possible.