Why do airplanes have rounded windows?
A pressurized fuselage needs rounded corners at all cut-outs to avoid the accumulation of stress in corners. If the corners were not rounded, the fuselage skin would need to be locally reinforced, or it would begin to crack there soon.

This was learned the hard way by de Havilland, when their Comet jet airliner began to plunge out of the sky for unknown reasons. In one of the first major crash investigations in aviation history, the wreck of one was lifted from the seafloor off Elba and re-assembled. Then it was learned that the pressurized cabin had burst from cracks emanating from the window corners.



de Havilland Comet I. Note the square windows. The window which caused the destruction of G-ALYP was on top of the fuselage and cannot be seen in this picture. (Picture source)



Finite element simulation of corner stresses in a Comet fuselage skin.  Red denotes the highest stresses. (Picture source)

Other aircraft companies had built pressurized cockpits twenty years earlier and did it right the first time …