Yet we can never do that. Why do you think?
The obvious answer in a classical universe is that we simply don't know the velocity and position of each particle, so we can't just reverse them. To pull such a feat, we'd have to be incredibly lucky, as in "winning every lottery for a century" lucky.
With entanglement and de-coherence however, such reversal becomes impossible even in principle: see, when the universe splits through de-coherence, you no longer have access to the other half. Even if you manage to reverse your half of the universe, you need the other half to be reversed too, or they'll never merge back together.
And not just the other half, since de-coherence happens all the time. You need all the Everett branches to be reversed. No. Way. So it does look like a better candidate for the arrow of time.
(Of course, a better candidate still would be collapse interpretation, since that one is not time reversible in the first place. But this interpretation is ridiculous to begin with, so let's ignore it.)
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Read this to have an idea of how time could work in a timeless universe: http://lesswrong.com/lw/qr/timeless_causality/