The strong field nature of the $CN^-$ ligand is due to its $\pi$-acceptor behavior. In addition to donating a lone pair of electrons to form a $\sigma$-bond with the central metal atom/ion, it can also accept electron density from the filled $d$-orbitals of the metal ion into its vacant antibonding $\pi^*$ orbitals through back-bonding. This synergic interaction increases the crystal field splitting energy ($\Delta_0$), making $CN^-$ a strong field ligand.