How can fear be dangerous in "Once Upon a Time"?

In Nadine Gordimer's “Once Upon a Time,” fear proves to be the family’s downfall. A family lives in a city in which there is great social unrest—modeled largely on South Africa—and fears riots and burglaries. Once further security is suggested by the husband’s mother, described as a “wise old witch,” the couple find themselves in an escalating war against their own fear. A neighborhood watch program is not enough to assuage their fears, so they get an electronically controlled fence. Having noticed a hole in one aspect of their security, they seek to mend it. Ironically, many of these measures make them more vulnerable, such as the alarms:

The alarms called to one another across the gardens in shrills and bleats and wails that everyone soon became accustomed to, so that the din roused the inhabitants of the suburb no more than the croak of frogs and musical grating of cicadas' legs. Under cover of the electronic harpies' discourse intruders sawed the iron bars and broke into homes, taking away hi-fi equipment, television sets, cassette players, cameras and radios, jewelry and clothing, and sometimes were hungry enough to devour everything in the refrigerator or paused audaciously to drink the whiskey in the cabinets or patio bars.

Quite plainly, the alarms cause more problems than they solve; however, the family does not appear to realize this fact. Their fear outweighs their common sense.
 
Near the end of the story, the family possesses an electronically-controlled fence, alarms, a seven-foot tall fence, and trusted employment: they ought to feel safe. The sight of their cat scaling the fence causes their security concerns to well up again, so they choose to arm the top of their fence with a vicious wire coil. Their child, after reading Sleeping Beauty, tries to make his way through the thorns to find a princess, but instead gets caught in the razors; he dies as a result.
 
Fear is the rationale behind the family’s actions, and look where it brought them: their only child is dead, indirectly by their hand. They do not even have the satisfaction of knowing that their efforts kept them safe, because they so clearly didn’t. Their internal desire for safety outpaced the actual threat at hand—in other words, their fear was disproportionate—and it led to the loss of their child.