Turn off the boat's engine and lift it out of the water. Now fling it into the air. It will then rotate around its center of mass.
Or around any other reference point you choose to describe its motion.
Neither is the center of mass, if you fling something it into the air.If you do that, then the reference point won't be stationary.
It is said that rocket,plane rotate about center of gravity ,why this is is not case for boats?
Boat pivot point is not in center of gravity.