Let's assume that the wire here is very long and very straight. There is a nice argument based on symmetry which suggests that the magnetic field around the wire have to be concentric circles.
Let us suppose that the magnetic field were not concentric circles, but concentric squares or "off centre" circles. Now, we rotate the wire along its axis by a few degrees. Since the wire rotates, the orientation of the magnetic field in space should also change, right?
But, we can also argue that the magnetic field should not change, because the appearance of the wire has not changed. Two perfectly logical and valid lines of reasoning have produced contradictory results!
The only way to resolve this contradiction is to postulate that the magnetic field around the long, straight wire form concentric circles.
The bar magnet does not have the rotational symmetry of a long, straight wire, so the above reasoning will not apply to it.