Why don't two magnetic field lines intersect each other?
Two magnetic field lines do not intersect each other because if they did, it would mean that at the point of intersection, the compass needle would point towards two directions at the same time.
This is not possible because the magnetic field at any point has a unique direction. A compass needle or a north pole placed at that point can only point in one direction. Therefore, no two field-lines are found to cross each other.
Explanation
The textbook explicitly states that 'No two field-lines are found to cross each other. If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible.' This is because the direction of the magnetic field is defined as the direction in which a north pole of the compass needle moves inside it. Since a compass needle can only point in one direction at any given point, field lines cannot intersect.