Question

why do not the magnetic field lines intersect each other

Answer 1

If magnetic field lines intersect each other then the magnetic field will have two different directions at that point that means there is a two direction in North Pole or South PoleThis is not possible. So they don't intersect.

Answer 2

If two magnetic lines of force intersect with each other than there would have been two directions of magnetic field at the point of intersection, which is not possible.