We investigate the time evolution of the six-component electron pressure tensor in a hybrid code studying consequences for the two-dimensional reconnection process in an initially perturbed Harris sheet. We put forward that two tensor components (a diagonal and a non-diagonal one) grow in an unstable way unless an isotropization operator is considered. This isotropization term is physically associated with an electron heat flux. As a consequence, we put forward that an enhanced value of a diagonal component is observed in the very middle of field reversal at sub-ion scale. Because of the increase in the kinetic pressure, the magnetic field is decreased in this electron layer, hence increasing the associated out-of-plane current at its edges and leading to its bifurcation. The bifurcation mechanism is based on the presence of electron pressure anisotropy, related to the gradient of inflow electron bulk velocity. The gradient in the inflow direction of the enhanced diagonal electron pressure tensor component results in the deceleration of the ions entering the X-point region. We suggest that bifurcated current sheets resulting from the anisotropies/agyrotropies of the six-component electron pressure tensor correspond to smaller reconnection rates compared to non-bifurcated ones.