It's an interesting question, where does the wear come from. But sails are a very active part of the boat; every tack is going to drag the sail across the deck of the boat, rub against fittings. When a sail luffs, head-to-wind it's whipping around with the weight of the sheets (control lines), and then when you're taking the sail down it's getting folded (best case) or stuffed into a bag (worst case) [EDIT: some sail materials like being shoved in a bag!]. And of course even when a sail is just sitting there powering the boat it's under a tremendous amount of force, which stretches it over time.
Sails do fail, and yes often by ripping in half. I've personally never heard of a sail failing at the control points (e.g. the tack of a jib), probably because those areas are heavily reinforced.
Those areas where the sail needs to be strongest is where they are re-inforced doubling up the layers (and not just 'two', a corner can easily be 10 ply or more thick), on older boats further re-inforced with leather or heavier grades of fabric. The panels are carefully laid out so that the highest stress aligns with the warps. A large sail can be made up from many 10's of panels, which are joined in a variety of manners (glue (typically for very fast boats or as re-inforcement of stitching), stitching, sometimes ultrasonic welding for special applications). On the very high end there are even laminated custom laid out fibre pattern sails (for instance: a sandwich of Kevlar wire between two layers of bonded fabric or plastic).
At one time I worked for a competitor of North Sails, who by the way were pioneers in the digitization of sail manufacturing.