Why doesn't the aviation industry use SI units?
Non-SI is only used for altitude, distance and speed except in US and some other American countries.


Altitude is in feet because 1000 ft happens to be reasonable vertical separation and 1000 ft is easier to calculate with than the corresponding SI figure 300 m. Also the procedures for instrument flying were first developed in the USA using feet.
Distance is in nautical miles because it is related to the unit used for measuring latitude and longitude. 1 nautical mile corresponds to 1 minute latitude (and longitude on the equator), which makes it easier to calculate distances from navigational maps using the grid lines as scale (large area navigation maps need to preserve angles, so they can't have constant scale). If angles were converted to decimal, 1 km would be 1/100 gradian. Alas, angles and time were never converted to decimal.
Speed obviously based on the distance unit in use.


Nevertheless if it was not for the prevalence of US-built planes after WWII and more advanced state of aviation in the USA at that time, we would probably be using metric in Europe too as continental planes before WWII usually had instruments in metric.