The flying ice cube effect is a molecular dynamics simulation artifact in which the use of velocity rescaling thermostats sometimes causes violation of the equipartition theorem, affecting both structural and dynamic properties. The reason for this artifact and the conditions under which it occurs have not been fully understood. Since the flying ice cube effect was first demonstrated, a new velocity rescaling algorithm (the CSVR thermostat) has been developed and become popular without its effects on the equipartition theorem being truly known. Meanwhile, the use of simple velocity rescaling and Berendsen (weak coupling) thermostat algorithms has not abated but has actually continued to grow. Here, we have calculated the partitioning of the kinetic energy between translational, rotational, and vibrational modes in simulations of diatomic molecules to explicitly determine whether the equipartition theorem is violated under different thermostats and while rescaling velocities to different kinetic energy distributions. We have found that the underlying cause of the flying ice cube effect is a violation of balance leading to systematic redistributions of kinetic energy under simple velocity rescaling and the Berendsen thermostat. When velocities are instead rescaled to the canonical ensemble's kinetic energy distribution, as is done with the CSVR thermostat, the equipartition theorem is not violated, and we show that the CSVR thermostat satisfies detailed balance. The critical necessity for molecular dynamics practitioners to abandon the use of popular yet incorrect velocity rescaling algorithms is underscored with an example demonstrating that the main result of a highly cited study is entirely due to artifacts resulting from the study's use of the Berendsen thermostat.