How can air travel be so safe if the aircraft skin is only 1-2 mm thick?
Simple maths. Cut a cabin in two, lengthwise, and check the forces involved. The halves are held together by 4mm of aluminium, and need to withstand a pressure differential wrt to the outside over the diameter of the cabin.

Let's assume that we have a wide body plane of 6m diameter (larger than a Boeing 777), and a pressure differential of 1atm (of course, usually a plane only maintains up to 0.8atm and does not fly in a vacuum, but let's have some safety margin).

The resulting tensile stress is then about 150MPa. Aluminium only yields at 275MPa.

Other forces are carried by struts, spars and in the case of the fuselage, stringers. The skin transfers shear forces between those perpendicular stringers, but I do not think those forces are significant compared to pressure loading.