As I recall the actual tether was quite strong, the superstructure surrounding it that housed linear electric motor bullet trains for transporting people and material to and from the geosync anchors. It fell apart because an idiot thought it would be a good idea to fire on it with a surface bombardment cannon with the destructive potential of a large nuke. And despite this, the tether held, it was the superstructure that was ejected to maintain the stability of the structure so wall sections the size of city blocks started raining down on the surrounding population center that had grown up as a result of the construction project.