Why does the FFT of a complex variable create negative frequencies?
It's about the type of signal being analysed. 

It's known from signal analysis that a real valued signal's Fourier transform is conjugate-symmetric $H(w) = H^*(-w)$ ; i.e., its positive frqeuencies are conjugate's of its negative frequencies. Hence it's not necesary to plot the whole spectrum, but just the positive half ot it is sufficient.

However, a complex signal's Fourier transform does not posses this symmetry property and the whole spectrum would contain relevant information about the signal, therefore you should consider not only the positive frequencies but also the negative frequencies when you analyse a complex valued signal.