  In this short note, we prove that $v(-\epsilon)=-v(\epsilon)$. Here,
$v(\epsilon)$ is the speed of a one-dimensional random walk in a dynamic
\emph{reversible} random environment, that jumps to the right (resp. to the
left) with probability $1/2+\epsilon$ (resp. $1/2-\epsilon$) if it stands on an
occupied site, and vice-versa on an empty site. We work in any setting where
$v(\epsilon), v(-\epsilon)$ are well-defined, i.e. a weak LLN holds. The proof
relies on a simple coupling argument that holds only in the discrete setting.
