This has been brought up numerous times but I don't really understand it. Consider a rod in freefall.
If you put your coordinate frame in the center of mass of the rod, there will be no torque around it and the rod as a whole will follow a straightline down. But now put a coordinate frame on one of the end points. Apart from the gravity pulling down on the rod as a whole, there will now be a net torque on the rod (because gravity acts in the center of mass).
What goes wrong with this picture, because clearly the rod doesn't rotate!