Loschmidt's paradox
In 1876 Loschmidt objected to the H-theorem on the ground that it should not be possible to deduce a time-irreversible process from time-symmetric dynamics. This was because for every path in a system that leads to an increase in entropy there is a reverse path that reduces it.
The apparent paradox is explained by the H-theorem's reliance on the "assumption of molecular chaos", which turns out to be time-asymmetric (see cross-linked element dealing with this assumption).