An analysis is made of the phenomenon of self-induced erosion and spectral breaking of ionizing high-power microwave pulses propagating in a gas. The analysis describes in an analytically explicit and physically clear way the consistent interaction between the microwave pulse and the self-induced breakdown plasma. In particular, it clarifies, both qualitatively and quantitatively, the mechanisms behind the pulse erosion and the spectral breaking phenomenon, i.e. the splitting of the pulse spectrum into a redshifted and a blueshifted peak as observed in numerical simulation results as well as in experiments.