Why doesn't current flow in reverse biased diode?

The current flows shown in the diagram are only temporary and flow only when the battery is first connected.

When you first connect the battery holes flow to the left (in your diagram) and electrons flow to the right, and the resulting charge separation creates a potential difference across the depletion layer. The flow stops when the potential difference across the depletion layer becomes equal and opposite to the battery potential. At this point the net potential difference is zero so the charges stop flowing.