Question

why don't two magnetic lines of force intersect each other

Answer 1

Two magnetic field lines can never intersect because if they intersect then there will be two tangents at the point of intersection which is not possible because Magnetic compass will show two direction.
So Two Magnetic Field Lines Can Never intersect each other

Answer 2

two magnetic feild lines could not intetsect each other because at the intersection point two tangants drawn which represent two direction of magnetic feild i.e. not possible