It's pretty simple: the forces at the anchor points would be infinite because of the 90°
angle ;-)
An example:
Imagine two pillars with the same height. If you attach a rope on both of them and try to tighten it, you will slowly increase the pulling force at the top of the pillars while increasing the angle between rope and pillar.
To fully straighten the rope, you need to achieve the 90°, which is not possible, since the force should be infinite (tan(90°)
) due to gravity. In fact, either the pillars or the rope will break…
Now imagine, that a rope is made of tiny particles (which actually is quite true ;-) and append the same logic on these subsystems of the rope.
In the case of the guy on the zip line, there is seemingly no near 90° angle, but in fact every piece of tiny "rope/pillar"-systems is suffering under this tension problematic. Without gravity, there is no problem to straighten such a rope…
I hope I could describe it clearly, maybe a picture would help!