1 They don't look good in pictures
Some people look good in pictures, while others look bad. The way the camera lens captures a person can result in a drastic shift in the way he looks.
2 They don't understand that a 2D picture is different than a 3D picture
The camera shows 2D pictures of 3D humans. Thus the camera doesn't show a person's real picture, while a mirror does. People who aren't aware of this fact might believe that they are ugly and hate appearing in pictures.
3 Fear of death
Some people hate to appear in pictures because on the unconscious level, they are so afraid of death that they don't want anybody to see their pictures after they are dead.
4 Body dysmorphic disorder
The body dysmorphic disorder or the imagined ugliness disorder can discourage people from appearing in pictures because of believing that they are ugly. (See Why do I look ugly from the side?)
5 Privacy concerns
In the internet age, photos circulate on the web in seconds. Some people hate to appear in pictures in order to not let others know the details of their private lives. (See Why Do People Care About Online Privacy?)
6 Mere exposure effect
People find their mirror picture more preferred because they are familiar with it. According to the mere exposure effect theory, people find camera pictures odd looking because they don't look familiar to them.
7 Loss of control
Once a picture is taken, especially by someone else, the picture can appear at unwanted times and places. Some people hate it when people take pictures of them because of the loss of control.
8 Not being able to select the angle
Some people look good in pictures only when they are taken from certain angles. Those people hate to appear in group pictures because they have no control over the angle.