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 physics of antennas plays a large part. To understand this, you must consider the Fourier transform of your signal. For a simple binary NRZ code, where 0 is 0V and 1 is some voltage, Most of the Fourier energy is contained within the frequency range 0-B/2, where B is your bitrate. But antennas are frequency-selective: at the high end, an efficient non-directional antenna has an effective signal collecting area that declines as the square of frequency. At the low end, efficiency suffers if the antenna is much less than a wavelength in dimension. The entire story is much more complicated than above, but any attempt to ameliorate the frequency dependence in some parameters increases the frequency dependence in other parameters. However, an antenna where the ratio of the highest to lowest frequency of operation is small can have nearly constant parameters over that narrow frequency range. Unfortunately, the NRZ signal has a **infinite** ratio, since the lowest frequency is zero! Any attempt to send a NRZ signal directly through a pair of antennas will yield an extremely distorted signal.

The usual cure is to modulate a wave that has a frequency, f, that is at least several times your bitrate. This moves the Fourier energy up to a band, perhaps f±B/2, with a small ratio of highest to lowest frequency. Then, antennas are well behaved, and you may recover the received data with a demodulator.
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.