New Fan Switch Grounding Cable issues
There is almost certainly a ground leak somewhere. It sounds like you might have a loose wire/bad connection in the fan's electrical connections.  Turn off the breaker and reconnect all the wires in the fan's electrical box.  If this doesn't work, you may need to take the fan down and take all the electrical components apart to inspect... or get a new fan.  It is not safe to run the fan without the ground attached, as the metal parts are likely charged.