If the magnetic lines of force intersected each other, then that would violate the laws of physics.
If the lines intersected, then at the point of intersections there would be two directions of magnetic field force, and this cannot defy the laws of physics, so therefore it does not happen.
A good example of this would be if you had a compass and you tried to use it to view the field direction. If you had two lines of force intersecting, then the compass would have to point in both directions, and that can't happen both theoretically and through observation.
An event like that would generate a monopole, which is an impossible, theoretical magnetic event.
