At high altitudes, I am speaking in like Tibet or the Alps (I don't really know if it applies in an airplane since they have climate control, but would assume it does to some degree) the air has a much lower oxygen content, much lower humidity content and a waaay lower pressure.
This means that your body will need more oxygen and thus have to beat the heart faster, I guess this might put strain on the thin nasal membranes and capillaries. Anyways, the lower humidity content would dry out the tissue there which can make it more brittle and prone to crack, and finally the low pressure would mean that the relative pressure (difference between body and outside body) would put more stress on the tissue.