A geosynchronous orbit is a perfect balance of a satellite/space craft/space station in orbit at 35,786 km (22,236 mi) above Earth's equator, following the direction of Earth's rotation that takes one sidereal day (23 hours, 56 minutes, and 4 seconds) to orbit the Earth.
How can this satellite stay in orbit with a 22,000 mile ribbon of cable hanging off of it? No matter how light, how thin, how "carbon fiberish" it is, it will pull the satellite from orbit. That ribbon will easily weight thousands, even millions of tons that are constantly pulling the satellite from orbit. Then consider the torque exerted by the elevator when it starts its climb with how many tons of cargo on board of the elevator would also be jerking the satellite from orbit…
The video uses a "Yo-Yo" metaphor to explain how this elevator would work. This example is ridiculous since the yo-yo is being held "in orbit" around the speaker by centrifugal force.
I'm certainly glad we do not have to worry how wind might whip a "ribbon/rope/cable" around because we just won't give it a second thought…
Think about it…