High-harmonic generation in solids by intense laser pulses provides a fascinating platform for studying ultra-fast electron dynamics and material properties, where the coherent character of the electron dynamics is a central aspect. Using the semiconductor Bloch equations, we expound a mechanism suppressing the high harmonic spectrum arising from the coherent superposition of intra- vs inter-band contributions to the total signal. We provide evidence for the generality of this phenomenon by extensive numerical simulations exploring the parameter space of this coherent suppression of high harmonics in systems of massive Dirac Fermions. We supplement our numerical observations with analytical results for the one-dimensional case. Moreover, we demonstrate reentrant behavior of suppressed high harmonics upon increasing dephasing.