The following is a part of proof of lemma 6.2 in the book.
$f:X \to Y$ a projective birational morphism of normal varieties
$D$: Weil divisor on $Y$, $E$: exceptional divisor of $f$
$\mathcal{O}_X(1)$: very ample
We get an injection
$a:\mathcal{O}_Y(mD)=f_*(\mathcal{O}_X(m))\subsetneq f_*(\mathcal{O}_X(m)(E))$ for $m\gg 0$.
Why is this a contradiction if $\mathcal{O}_Y(mD)$ is reflexive and $a$ is an isomorphism outside the codimension $2$ set $f(Ex(f))$?