We show here that the application of potential barriers that induce contributions of hyperboloid subbands (pseudospin filters) in graphene nanoribbons locally breaks the chiral symmetry of the Dirac state, in the sides of the barrier, with the consequent transition from Klein to anti-Klein behavior. With the increased filter potential applied, resonances of Fabry-Pérot type with line widths that are decreasing are generated in the conductance, which is associated with a pseudospin precession located on the sides of the barrier. Interestingly, throughout this process the chiral symmetry of the state is conserved, and pseudospin oscillations (opposite) that increase in intensity are observed on the sides of the filter. This is associated with a gradual loss of the electron-hole correlation, with the increased filter potential, which ends with the formation of a transport gap when the electron-hole symmetry is completely broken. This is an example of how the chiral symmetry can evolve and still be conserved, during a tunneling process. All this leads to the generation of energy gaps, associated with anti-Klein tunneling, which can be controlled using certain spatial configurations of the applied filters. The inclusion of a new type of asymmetry (roughness in the filters) makes it possible to recover Klein's tunneling in the region of induced gaps. The interaction of the hyperboloid subbands with the Dirac band can be observed in density-of-states maps using the pseudospin filters, following the behavior of the van Hove singularities as a function of the filter potential.