If you read Why Do Clocks Run Clockwise? And Other Imponderables, and shame on you if you haven’t, you know that newspapers tear easily in a vertical position because all the fibers are lined up in the same direction when pulp is put into the papermaking machine. String cheese works on exactly the same principle.
When producing string cheese, the cheese curd is formed into a large mass and then stretched mechanically. The stretching causes the protein fibers to line up in a parallel fashion. According to Tamara J. Hartweg, of Kraft, “This physical modification of the protein structure is what causes the stringing quality of the cheese. When peeled, the protein fibers, which are aligned in one direction, come off in strings.”