We challenge the magnetar scenario for short gamma-ray bursts by performing a high-resolution neutrino magnetohydrodynamics numerical relativity simulation of a binary neutron star merger. We find the alpha Omega dynamo mediated by the magnetorotational instability generates the large-scale magnetic field in the merger remnant. The resultant large-scale field is efficiently wrapped and drives a relativistic Poynting-flux dominated outflow from the merger remnant.