If everything in the universe evolves toward increasing disorder, it must have started out in an exquisitely ordered arrangement. This whole chain of logic, purporting to explain why you can’t turn an omelet into an egg, apparently rests on a deep assumption about the very beginning of the universe: It was in a state of very low entropy, very high order.
The arrow of time connects the early universe to something we experience literally every moment of our lives. It’s not just breaking eggs, or other irreversible processes like mixing milk into coffee or how an untended room tends to get messier over time. The arrow of time is the reason why time seems to flow around us, or why (if you prefer) we seem to move through time. It’s why we remember the past, but not the future. It’s why we evolve and metabolize and eventually die. It’s why we believe in cause and effect, and is crucial to our notions of free will.
And it’s all because of the Big Bang.
And really, everything is just Science (okay, and Math)...even things like free will, and of course time, if you think about it.