Why Earth's atmosphere behaves like an ideal gas? In every book I found this sentence like an assumption, without explananions, somebody can help me understand it better?
 A: The Earth's atmosphere is mostly nitrogen and oxygen, both of whose behaviors are very close to ideal at the temperatures and pressures found in the atmosphere. Nitrogen, the dominant gas in the atmosphere, comes particularly close to exhibiting ideal behavior. Gaseous oxygen exhibits about a 3% departure at 20 atmospheres at standard temperature, with departures from ideal reducing more or less linearly at reduced pressures. 
There is one component whose behavior is markedly non-ideal, and that is H2O. Water vapor is a trace gas, at most a few percent of the atmosphere (and that extreme occurs only in very humid tropical regions). Unless you are studying cloud physics, you can pretty much ignore the departures from the ideal gas approximation. The errors that result from assuming ideal behavior are generally less than one percent.
Non-ideal behavior becomes important if you want to model the atmospheres of Venus or the gas giants because of the higher pressures. For example, the CO2 that is by far the dominant component of Venus's atmosphere is a supercritical fluid at the surface of Venus. Departures from ideal behavior can be quite extreme in this regime.
A: Look at the definition of ideal gas .

An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. One mole of an ideal gas has a volume of 22.7 L at STP (standard temperature and pressure).
At normal conditions such as standard temperature and pressure, most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated like ideal gases within reasonable tolerances

From the list and knowing the composition of the atmosphere one can see that the simple classical model of non interacting elastically scattering molecules is good enough for  most purposes. Even though there exist interactions and scatterings follow quantum mechanical laws, to first order the ideal gas is a good approximation.
It is an assumption, but a good approximation of what is going on really.
A: Any gas behaves as an ideal gas under high temperature an low pressure. Atmospheric oxygen is at 25deg celcius which is greater than it's critical temperature which is -150 deg celcius. And the pressure is somewhere around 159 mm of Hg (21.1 kPa). Hence atmospheric gases is said to behave like that of an ideal gas.
