Why do 3 protons need to pass from the intermembrane space into the matrix of the mitochondrion in order to form 1 ATP molecule?

It has to do with the structure of the ATP synthase protein. The part in the centre moves 120 degrees with each prototon that passes through. This makes the 3 ATP/ADP binding sites to change shape. Each of them goes in turn from the shape in which ADP and inorganic phosphate are caught, to the shape which promotes ATP formation and, finally to the shape which releases the ATP.