About the measure of security in Section 7.1

I have a second question.

In the 7.1 section, the authors discuss possible application. They claim that the ratio S/\epsilon is a measure of security. Why is it so? Why \epsilon is not a measure of security? The authors set S/\epsilon = 2^n. If I want a negligible probability for \epsilon then my circuit is of size 2^{2n}? Am I missing something?