Allah says:
So whoever Allah wants to guide - He expands his breast to [contain] Islam. And whoever He allows to stray - He makes his breast tight and constricted as though he were climbing into the sky. Thus does Allah place defilement upon those who do not believe. (6:125)
It can be concluded from this verse that the more one ascends into the atmosphere the harder it is for him to breathe. This is due to the reduction in pressure and low oxygen levels. This matter cannot be proven by anyone unless the person ascends up into the sky! This fact was discovered only after humans learned how to fly and reach heights.
When a person ascends into the sky beyond eight kilometers above sea level they would encounter breathing problems due to the lack of oxygen and low air pressure. A problem frequently encountered is hypoxia, which is a low amount of oxygen reaching body tissues.
Another problem one may encounter is dysbarism, which is a complex of symptoms resulting from exposure to excessively low or rapidly changing air pressure. These two problems would interfere with normal body functions. Therefore, the difficulty in breathing at high elevations can be explained simply as steps taken by the body to protect itself.