Why is Henry afraid of the cage that runs up the center of the stairwell at the Newberry Library in the novel, The Time Traveler’s Wife?

The cage at the Newberry Library is four stories high and runs up the center of the stairwell. Made from steel and sealed, it frightens Henry because if he gets in there he will not be able to get out. The cage is assumed to be there as a prevention for falling down the stairwell center.