In this paper I shall shed some doubts on a widely-held claim: standard quantum mechanics is time-reversal invariant, and thereby, blind to the direction of time. Building bridges between physics and philosophy, I shall argue that such a claim features some puzzling assumptions that are frequently overlooked in the literature. In particular, I shall first argue that the claim involves some methodological and metaphysical commitments that should be evaluated more prudently from philosophy and from physics. Second, I shall point out that the common inference that goes from symmetry to metaphysical conclusions needs some correction and refinement to be acceptable for time symmetry and the debate around the arrow of time.