  In a recent paper \cite{Ablikim:2019pit}, the BESIII collaboration reported
the so-called first observation of pure $W$-annihilation decays $D^+_s \to
a^+_0(980) \pi^0$ and $D_s^+ \to a^0_0(980)\pi^+$. The measured absolute
branching fractions are, however, puzzlingly larger than those of other
measured pure $W$-annihilation decays by at least one order of magnitude. In
addition, the relative phase between the two decay modes is found to be about
180 degrees. In this letter, we show that all these can be easily understood if
the $a_0(980)$ is a dynamically generated state from $\bar{K} K$ and $\pi \eta$
interactions in coupled channels. In such a scenario, the $D^+_s$ decay
proceeds via internal $W$ emission instead of $W$-annihilation, which has a
larger decay rate than $W$-annihilation. The proposed decay mechanism and the
molecular nature of the $a_0(980)$ also provide a natural explanation to the
measured negative interference between the two decay modes.
