How does a chordae tendinae rupture?

Usually wear & tear. Most cases of chordae tendinae rupture are because of degeneration after years of routine "wear and tear" leads to thickening and retraction. Rarely, it can occur due to infection (endocarditis), either acutely, or later if fibrosis develops and distorts the chorda. If a mitral valve is extremely "floppy", i.e. Mv prolapse, the flopping leaflet may pull the chorda hard enough to tear it.
Myxomatous degen. It occurs in the setting of myxomatous degeneration, an inherited disorder of collagen, manifest premorbidly by long, redundant chordae and a floppy mitral valve (causing easily detected mitral valve prolapse). Rupture is a random event and may result in anything from no symptoms (rare) to new onset atrial fibrillation and acute congestive heart failure, sometimes with pulmonary edema.