I think it is quite simple.
1. each part of the magnet is a magnet itself, thus they generate there own field lines, and they are so not necessarily supposed to coincide with the axis.
2. the field line formed are in curves and so they do not parallel to the axis of the magnet.
3. also, the lines coming out directly from the point coinciding with the axis (i would prefer it to call the center of the, just take, bar magnet), will seems to run coinciding with the axis, will not keep on coinciding for a long distance. it will get the loop to meet the other side, that is the unlike pole side.