The dominant roles of pressure tensors in collisionless magnetic reconnection are demonstrated during a steady state of two-dimensional collisionless driven reconnection without any guide field by means of full-particle simulations. The pressure tensors in the momentum equations of ions and of electrons play two crucial roles in the collisionless magnetic reconnection. One role is the gyroviscous cancellation which suppresses the violation of frozen-in condition due to the inertia term. This cancellation causes ions to be tied to the magnetic field within the ion skin depth. The gyroviscous cancellation of electrons is also observed. The other role is a strong violation of the frozen-in condition due to non-gyrotropic pressure. The strong violation of the ion frozen-in condition forms the ion-dissipation region where the collisionless magnetic reconnection occurs. The strong violation of the electron frozen-in condition generates the reconnection electric field at the reconnection point.