Reversing the direction of a ceiling fan does not damage the fan motor. In fact, most modern ceiling fans are designed to be reversible, and they come with a switch that allows you to change the direction of the fan blades easily.
When you reverse the direction of the ceiling fan, it changes the airflow pattern in the room. In the standard forward (or "summer") direction, the fan blades rotate counterclockwise, creating a downward airflow that provides a cooling effect by creating a wind chill effect on your skin.
When you switch the direction to the reverse (or "winter") mode, the fan blades rotate clockwise. This upward airflow helps to redistribute warm air that rises to the ceiling, back down towards the living space. As a result, it can improve the efficiency of your heating system and make the room feel warmer during colder months.
Reversing the fan's direction does not cause any harm to the motor or the fan itself. It's a feature built into the design of most ceiling fans, and you can switch between the two modes as needed without any adverse effects. However, it's always a good idea to refer to the fan's manual or consult the manufacturer's guidelines to ensure you are operating the fan correctly and safely.