Assumption of molecular chaos
The H-theorem is invalidated by its reliance on a time-asymmetric assumption: the Stosszahlansatz ("assumption of molecular chaos"). This is the assumption that probabilities of velocities of colliding particles are independent.
The molecular chaos objection explains Loschmidt's paradox (joined to this element by a Consistency cross-link) which draws attention to the fact that it should not be possible to derive a time-irreversible process from underlying time-symmetric dynamics. The explanation is that the molecular chaos assumption is inherently time-asymmetric.