Multiple Equilibria and Index Theorem
What about
\begin{array}{|c|c|c|}
\hline 
&amp;C&amp;R\\\hline
M&amp;0,0&amp;0,0\\\hline
D&amp;0,0&amp;1,1\\\hline
\end{array}
?

This game has two pure equilibria, $(M,C)$ and $(D,R)$ but no mixed equilibra.

You are probably referring to Wilson's Oddness Theorem, which guarantess your claim for generic games. See
Oddness of equilibrium points.