A fan that has always been in the room can suddenly look or sound different to a dog. The light, shadow, vibration or another recent frightening event may matter. You do not have to decide which from one episode. Do not lift the dog toward the fan or touch it while insisting they watch.
Turn the fan off if it is safe to do so and let your dog leave the room. Make another comfortable place available. Check whether the fan is loose, rattling or otherwise unsafe without making your dog inspect it. If this fear appeared suddenly, is intense, or your dog is also acting differently around other sights or sounds, ask your veterinarian about pain, sensory change or illness.
Once the dog is well and the equipment is safe, notice whether they can relax at a distance from the fan when it is off. Reward a calm look and move away together. Do not switch it on as a surprise to see what happens. A qualified reward-based trainer can help if the room is hard to avoid or the fear spreads. The noise-fear guide may be useful if sound is part of a wider pattern, but a medical check comes before sound exercises for a new severe fear.
Today, give your dog a fan-free place to rest and write down what changed just before the fear began. That is more useful than proving the fan cannot hurt them.
Sources: VCA on new fear, health and sensory changes. VCA on fear of places and avoiding forced exposure.