Question: Like ethernet cable, optical fiber. We have a square wave signal, do we just send that squre-wave signal directly down along the cable? If we do send it directly, why we can not send the square-wave signal directly into the air wireless channel? What is the reason behind? Is it because the cable or wire are more stable but wireless is very unstable?

Answer: 
The voltage or current you apply at one end of a pair of wires can be detected directly at the other end. It's like pulling on one end of a tight string -- you can feel the pull at the other end.

When communicating wirelessly there is no quality of the source that can be directly felt or measured at the other end. It's like you're standing in one end of a pool. You can hold your hand at any height and the water at the other end is unchanged -- the height of your hand is undetectable. If you move your hand up and down rapidly, however, you can make a *wave* that propagates to the other side of the pool where it *can* be felt and measured.
None of them are actually a square wave. They all are approximations. It would take a noise free channel with infinite bandwidth to transmit a true square wave.