Look at that $\ce{RO-}$. It is a base, right? A strong base. A strong base is likely to attack an acid. In this case, the most acidic hydrogen is the one which is the one in $\ce{CHCl2}$ (See explanation below). For convenience, let's call it $\ce{H-\alpha}$ and the other two $\ce{H-\beta}$.

(The base shoud be $\ce{RO-}$, but the drawing tool I'm using does not support placeholder signs.)
Now we have this:

This is called E1cb mechanism. (cb stands for intermediate carbanion)
Why is the hydrogen attacked
$\ce{H-\alpha}$ has totally three -I effect group: two chlorine and a fluoromethyl group. Meanwhile, $\ce{H-\beta}$ only has two -I effect group: a fluorine group and a dichloromethyl group. Therefore, the intermediate is more stable than it would be if $\ce{H-\beta}$ is eliminated.