Why 180 degrees of phase margin should be considered?
Do not follow your plots but let me address your block diagram and question in heading. The 180 degree reference is convention. A feedback block diagram, not shown in yours, generally shows a subtractor combining the input with the feedback signals going back to H. Black. It also emphasizes the fact that we generally want 'negative' feedback to stabilize the system response. As such, the algebra for the transfer function becomes: H=G(s)/(1+Beta*G(s))
In your example, Beta=1.

Now, the critical condition is when the denominator goes to zero and the phase and gain margins quantify how closely the denominator gets to this condition. What is the phase of Beta*G(s) at the frequency where this quantity has unity magnitude, and what is the magnitude of this quantity when the phase goes to _+180 degrees? 

If the phase is +-180 degrees when the magnitude is 1 then we get the infinity, division by zero, at phase margin zero. If the magnitude is 1 at the frequency where the phase is +-180 degrees we again get infinity where gain margin is 0. So the 180 depends on introducing the SUBTRACTOR at the combination point of input with feedback signal. 

If on the other hand, we use a SUMMER to combine the signals (no subtraction), we get: H(s)=G(s)/(1-BetaG(s)) and the critical angle is ZERO degrees and phase margin is found as the phase difference of {BetaG(s)-0} at the frequency where the magnitude of BetaG(s) goes to 1. G(s) contributes to the phase-magnitude vs frequency shape of the Loop Gain, BetaG(s). 

The literature generally includes the external subtraction. Personally, I prefer the summer as this puts the total phase change in the electronics and is not offset by the external algebraic subtraction. Since phase margin is the phase referenced to the critical phase, 180 for using a subtractor, 0 for using a summer, the result is the same. Since the literature is biased to the subtractor, one needs to make it clear when using a summer that the reference angle is 0 and not 180.