Say e(t) is sine wave and y(t) is sine output.
If y(t) has the same frequency as e(t) with phase shift of 180 degrees, we can only get stability of the system, if the gain of open loop at this frequency is less than 1.
This makes sense to me, in order for y(t) to gradually descend toward 0, the gain obviously has to be less than 1.
In order for that to happen, the polar plot of open loop G(iw) at this frequency (where it crosses the (-x)) has to lie between points (-1,0) and (0,0).
Why? What does the location of that exact point tell me about gain of this system?