The large inertia of the roll helps it to stay at rest. The sharp jerk is a large force, which exceeds the breaking strength of the paper. The paper is unable to transmit the force without shearing, and it tears where it is designed to do so, at the perforation. If you exert a gentle pull, the paper transmits that small force. You will cause a small (angular) acceleration and the roll will unwind instead of tearing.
Work Step by Step
See the hanging ball and string demonstration in Figure 2.5 (page 26).