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In a recent paper [1], the BESIII Collaboration reported the so-called first observation of pure W-annihilation decays Ds+→a0+(980)π0 and Ds+→a00(980)π+. 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 a0(980) is a dynamically generated state from K¯K and πη interactions in coupled channels. In such a scenario, the Ds+ 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 a0(980) also provide a natural explanation to the measured negative interference between the two decay modes.