Swinging a marble at the end of a string.
As we all know it is centrifugal force what makes the marble turn around, isn’t it?
If we remember Newton’s first law when we put an object in motion it wants to keep moving in a straight line in the same direction, and with the same speed. To make that object (a marble in this experiment) turn in a circle we must apply it a force, and since once it is in motion the marble wants to always move in a straight line, to make it turn around we must apply a force to constantly change its direction of motion. The force needed to achieve that constant change of direction must be towards the center. This force is known as centripetal force (centripetal meaning precisely “towards the center”). Just centripetal force applied by the hand and inertia of the marble itself keeps the marble swinging around. No centrifugal force at all.
In the same way, in fly casting, line’s inertia and the force exerted by the rod tip is what makes the loop form and turn over.