While determining the phase cross over frequency, why is it taken at -180degrees only? why not any other angle?
-180 degrees is where negative feedback instability or oscillations occur since, at that point, the negative feedback becomes positive.
With respect to instability it's normal practice to consider the gain margin at the 180 degree phase transition. This combination of gain & phase informs one as to the likelihood of potential instability.
Most feedback circuits use an amplifier with inverting gain and this yields 180 degrees phase shift. If the feedback circuit contributes another 180 degrees phase shift, the total circuit phase shift is 360 degrees, otherwise the feedback is in phase and the circuit will oscillate if the gain is high enough. Thus, the 180 degree phase point is critical because it is the point at which oscillation occurs, but after 135 degrees phase shift the output becomes subject ringing etc. so the range between 135 and 180 degrees phase shift is often looked at in detail, but that is something you will probably learn in another class. Remember, oscillation always occurs when the phase shift reaches 180 degrees if the gain is equal to or greater than one. When the gain is greater than one the circuit distorts the signal to drive the gain back to one.
http://www.ti.com/lit/an/snva020a/snva020a.pdf read pages 3 and 4 BTW: the "crossover frequency" is not defined as -180 degrees, it is the frequency where the loop gain is UNITY (which is 0 dB). The phase shift at unity gain determines if the loop is stable.