The shutter sound makes them twitch
Whenever they hear the sound of the shutter, they twitch by reflex (inherited from long ago when they were pray to a clicking snake). The twitch is faster than the shutter speed so that they always move out of the picture. They also hang out in the bright sun, where photographers use shorter exposure time, so there is no time for them to fly back into the picture before the shutter closes. If the exposure time is long enough for them to do that, the picture becomes way to bright to see anything anyway.
Why don't the photographer use a silent camera?
Because they don't know that fairies exist, so they don't know that there would be anything to take a picture of. Only professional photographers journey that far into the forest, and they bring those big expensive cameras where the click sound is part of the user experience.
Wouldn't fairies fly very far if the camera is distant?
The forest is so thick, that if the camera is say twenty meters away, they would end up behind bushes and leafs anyway. If they are so far away that they don't hear the camera, they end up too tiny on the picture for anyone to see them.