Consider a large community, structured as a network, in which an epidemic spreads. Infectious individuals spread the disease to each of their susceptible neighbors, independently, at rate λ, and each infectious individual recovers and becomes immune at rate γ. The social distancing is modeled by each susceptible who has an infectious neighbor rewires away this individual to a randomly chosen individual at rate ω. Our main result is surprising and says: the rewiring is rational from an individual perspective in that it reduces the risk of being infected, but at the same time it may be harmful for the community at large since the outbreak may get bigger compared to no rewiring (ω=0).