Question: [![enter image description here](https://i.stack.imgur.com/r18K6.jpg)](https://i.stack.imgur.com/r18K6.jpg)

This is an open circuit. Now, a chemical reaction happens in the cell which makes the current to flow in the wire. Then, the current has no other place to go, so it just gets grounded. It is similar to if I was holding the end of this circuit & put it on my finger. I would experience the current. So, the current does flow right. I do agree the circuit will not complete.

Why is it said that $I = 0$ in open circuit because of potential difference.

The charge inside the cell will move from the negative terminal to the end of circuit through chemical reaction inside the cell.

Answer: 
*Why is it said that I = 0 in open circuit . . .*

This is a steady state condition assuming that the resistance of the open circuit is infinite (very, very high).

The processes occurring in a cell are very complex.  

There is an electro-chemical reaction which results in charges being migrating from one electrode to the other.  

The imbalance in charge between the two electrodes leads to a potential difference across the electrodes which in turn results in an electric field between the electrodes.  

The electric field opposes the migration of changes between the electrodes and eventually, if the electrodes are not connected to the outside world, the migration of charges stops and a steady potential difference is set up between the terminals (the emf/voltage of the cell).

If a conducting circuit is connected between the electrodes of the cell an electric current flows whilst the electro-chemical reaction maintains a potential difference across the cell.  

This is the state when your circuit above has a complete conducting path.

Now suppose a break is made in the circuit.  

The current cannot stop instantaneously as the circuit has an inductance, but rather reaches the final steady state zero value over a period of time which in this instance will be very short.

In the final state the two ends of the open circuit can be thought of as a charged capacitor with the potential difference across it being equal to the emf of the cell and no current is flowing in the circuit.
There is indeed [a very brief moment](https://physics.stackexchange.com/questions/531183/does-an-electric-current-flow-in-an-open-circuit) when the wires are attached to the terminals when a current flows, during which the wires are brought to the potential of the terminal.

There is no current otherwise, because as you mention the circuit is not closed.