This is an interesting question to consider when thinking about this excellent short story. Of course, whilst the parents do face what they show fear about--the lions in the African scene that the children have created in their futuristic nursery--they do not choose to face this fear at all. Rather, their children manipulate and trick them into getting them into the nursery and then lock the door, ensuring their parents' death in the most horrid of ways.
Therefore, if I were you I would want to discuss the fear of the children in being taken away from the nursery which they have become so dependent on. Notice how Peter threatens his father when he suggests that they should have a "house-free existence":
"I don't want the nursery locked up," said Peter coldly. "Ever."
Also, when he makes this final decision to turn off all of the mechanical machines that have taken over their lives and had such a negative impact on their children, note Peter's reaction:
"Don't let them do it!" wailed Peter at the ceiling, as if he was talking to the house, the nursery. "Don't let Father kill everything." He turned to his father. "Oh, I hate you!"
However, in spite of this step in the right direction, the father crucially and fatally gives in, allowing his children one more play in the Nursery and thus sealing his own fate. So, when we think about facing fears in this excellent short story, the biggest fear is the children's fear of being without their nursery, which they never truly have to face.
I feel that one of the fundamental statements that Bradbury is making about facing one's fears connects to how parents interact with their children. Both parents in the story fear to speak their mind and face their fear of the reality that is creeping upon them. The children are too addicted to the room, to technology, and are severing the relationship with the parents. We see that the parents rationalize this in different ways, possess fear about upsetting the children, and face that fear by doing their best to placate them. Yet, all of this is done with the strict desire to avoid confrontation. I don't think that Bradbury wants us to blame the victims, the parents. Yet, rather I believe that he is stressing to the reader that despite all the technological marvels that he believes the future will hold, there are some fundamental issues that will not go away. Notice David's words on this front:
You’ve let this room and this house replace you and your wife in your children’s affections. This room is their mother and father, far more important in their lives than their real parents.
Parents' need to face their fears to guide their children, to open uncomfortable dialogue, and exert a force in which children understand the right and proper use of the available technology in the modern setting, which are all a part of these ideas. The fact that the parents do not face their fears invariably leads to their own deaths at the hands of their own children.