Type II radio bursts are observed in the Sun in association with many coronal mass ejections (CMEs. In view of this association, there has been an expectation that, by scaling from solar flares to the flares which are observed on M dwarfs, radio emission analogous to solar Type II bursts should be detectable in association with M dwarf flares. However, several surveys have revealed that this expectation does not seem to be fulfilled. Here we hypothesize that the presence of larger global field strengths in low-mass stars, suggested by recent magneto-convective modeling, gives rise to such large Alfven speeds in the corona that it becomes difficult to satisfy the conditions for the generation of Type II radio bursts. As a result, CMEs propagating in the corona/wind of a flare stars are expected to be radio-quiet as regards Type II bursts. In view of this, we suggest that, in the context of Type II bursts, scaling from solar to stellar flares is of limited effectiveness.