When I saw the scene, I imagined the cord and/or the parachute to be elastic. So even if the cord is taut, it may not be in a stable stationary state; the cord

When I saw the scene, I imagined the cord and/or the parachute to be elastic. So even if the cord is taut, it may not be in a stable stationary state; the cord might snap beyond a certain amount of stress or the parachute might unhinge. Infact, after Clooney's character unleashes himself, Bullock's character recoils back, which seems to agree with my elastic theory.