  We reanalyze the dissociation process of the $J/\psi$ by $\pi$ and $\rho$
mesons into $D + \bar{D}$, $D^* + \bar{D}$, $D + \bar{D}^*$, and $D^* +
\bar{D}^*$ within a meson exchange model. In addition to the dissociation
mechanisms considered in the literature, we consider anomalous parity
interactions, whose couplings are constrained by heavy quark spin symmetry and
phenomenology. This opens new dissociation channels and adds new diagrams in
the previously considered processes. Compared to the previous results, we find
that these new additions have only a minor effect on the $\rho + J/\psi$ total
inelastic cross section, but reduce the one for $\pi + J/\psi$ by about 50 %
near the threshold.
