cp violation - Why does the pion not undergo netural particle oscillation?

$K$, $B$ and now $D$ mesons exhibit neutral particle oscillation, where we see the spontaneous interchange between a particle and its antiparticle, i.e. $K^0 \Leftrightarrow \overline{K}^0$, $B^0 \Leftrightarrow \overline{B}^0$ and $D^0 \Leftrightarrow \overline{D}^0$.

My question is, why do neutral pions $\pi^0$ not exhibit the same behaviour? We never hear of "pion oscillation" $\pi^0 \Leftrightarrow \overline{\pi}^0$...

Answer

Answer transposed from a comment: the $K$, $D$, $B$ have nonzero "flavor quantum number" (strangeness, charm, and beauty, to be specific). The analogy you should pursue is the $J/\psi$ or "charmonium," made of a charm quark and charm anti-quark.