I want to reverse my fan from the winter mode (blowing are upward) to the summer mode (blowing air downward). With the remote, it will not change direction of the blades. Even if we turn of the wall switch, it still does not reverse.

Does the LED on the remote light when you try to reverse it?

Is there a switch anywhere on the fan body?

Should only reverse with fan stopped,
If it does not have a revesing fan switch and older, You may have to physically(with fan stopped)
Push blade in from end and twist blade for reverse air.

The fans you speak of are the old Hunter Reversaire fans. Those could not be operated with a remote.