The Onsager relations applied to electronic transport establish that the conductance of a two-terminal conductor is an even function of the applied magnetic field. However, breakings of this symmetry may take place in the nonlinear regime. We demonstrate that magnetoasymmetries arise in mesoscopic systems only as a consequence of the charge response of the conductor, thus being a pure interaction effect. Furthermore, we investigate magnetoasymmetries in the linear response regime when a mesoscopic system interacts with its environment. We show that the interaction between the two systems causes an asymmetry when the environment is out of equilibrium. Finally, we study the magnetoasymmetric current fluctuations of a quantum dot in the Coulomb-blockade regime. Interestingly, we find that the magnetoasymmetries corresponding to the leading-order nonlinear conductance and noise fulfill a higher-order fluctuation-dissipation relationship.