So, let's say for an isolated system I go from A to B thru a reversible path then entropy is zero. And if I go thru an irreversible path, it's something else. But if entropy is a state property, how can it be different for the two paths between same points? This completely makes no sense to me.[/QUOTE]
If entropy increases, the two paths will not link the same points. There is a set of points B which can be reached on reversible paths starting from A and there are other distinct states B' which can only be reached in irreversible processes.