Referring to the current as flowing towards or away is just a way of labelling directions on the diagram for our own convenience. Just as you would give directions with reference to North, South, East and West, in this diagram we make reference to upwards, downwards, left, right, towards and away. So we see the arrow is pointing in the direction we define to be towards us and if we draw arrows all the way around the loop, the current in the part of the circuit that passes through the magnetic field will be pointing in the 'away from us' direction.
There is no hidden physics behind why the current is flowing towards or away, it is purely just a way of defining a direction based upon the orientation of the diagram.