This is somewhat controversial issue. But let me present the reasons, as far as I understood, why people like Sir Penrose thinks so. Their arguments are roughly as follows:
1) The basic microscopic laws of physics are perfectly time symmetric. They are not biased in any time direction past or future.
2) Second law follows from the fact that that given an initial condition of a system which is not in the most probable state will tend to go towards the most probable state by the same microscopic laws. Since number of disordered states are much higher the system will become more and more disordered with time. Accordingly its entropy will increase until a maximum value when the system comes to the thermal equilibrium.
3) Since the microscopic laws are time symmetric the same argument can be made towards the past time direction as well. Given an an initial condition of a system which is not in the most probable state should go towards more disordered (high entropy) states towards past as well. That's what the mathematics of the laws tells us.
4) This is against our experience. Either all the parts of the universe we are observing (including our memories of past) has just undergone a HUGE fluctuation right now to give the impression that there was a more ordered past (which is crazy) OR the system was already even more ordered (low entropy) and more special in the past. But that means even more huge a fluctuation. This reasoning will lead us to conclude that at the moment of big bang the universe was extra ordinarily ordered and most special. It should be so special that it requires explanation.
Critics often point out that prediction and retrodiction is not the same thing forgetting that when one talks about the very "arrow of time" no one can say with justification which is prediction and which is retrodiction. Other than that it is also questionable whether second law can be applied this way to the whole universe or not.
This post imported from StackExchange Physics at 2014-05-14 20:00 (UCT), posted by SE-user user1355