A wobbly ceiling fan can fall off if 1) the screws attaching the fan to the junction box are not firmly attached or if 2) the ceiling fan was improperly installed in an electrical junction box designed for a light fixture instead of a fan. The weight of the fan plus the torsion during use can cause the fan to break free from the ceiling. Additionally, a wobbly ceiling fan can cause a light fixture to fall off and come crashing down, potentially causing injury.