This is an area of lively study. The cable is heap big flexible and can be maneuvered. Simulations have been done that show the cable can be moved out of the way of any satellites. (Don't assume that it is as simplistic as I describe. There's a lot more to it.)I have no doubt that a strong enough material will be developed. However, for a space elevator to be possible around the earth, we would have to first eliminate all of the sattelites in low Earth orbit. There is no point on the equator over which these sattelites will not eventually pass. When they do, they will strike the elevator shaft at about 15,000 miles per hour. If we hadn't done sattelites first, a space elevator would be possible. But as far as I have seen, no one has ever addressed this situation adequately. And, as the situation currently stands, a space elevator is simply not possible.