We have developed a simple but general analytical theory that elucidates the mechanism of spin-wave generation from interfaces between ferromagnetic media pumped by a uniform microwave magnetic field. Our calculations show that, provided there is a finite coupling between the two media, the amplitude of the emitted spin waves depends linearly on the difference between their magnetic susceptibilities. The theory is successfully applied to interpret qualitatively three recent experimental studies in which such a spin-wave emission was observed. Furthermore, we describe how our approach can be extended to several more complicated spin-wave excitation schemes employing electric, elastic, and optical stimuli.