Summary
A cup shatters but never reassembles by itself; entropy sets that direction. The drift from ordered states to more disordered ones reinforces our one way sense of time.
You sense time does not run backward even as a child: spilled milk does not jump back into the glass. Behind that intuition sits statistical physics.
Entropy relates to the number of microscopic configurations. Moving from order to disorder is vastly more probable.
So reversal is not forbidden, just astronomically unlikely. Even if atoms allow it, they will not all coordinate into order.
Entropy links thermodynamics to cosmology. The arrow of time is often drawn by probability, not by a strict ban.