You must keep in mind that virtually the entire width of the relatively flat tread of a car is in contact with the road all of the time. A car remains upright, even when cornering. This results in a much smaller contact footpring for a motorcycle tire. There are now two main reasons for directional arrows. The first being that some motorcycle tires now have tread patterns that are designed for a specific rotation for optimum performance, particularly on wet roads.
Directional arrows indicate proper directional rotation.
Secondly, running a tire will set up a wear pattern that may cause ride disturbance if reversed. The directional arrow insures that a tire can be re-fitted in the original direction. I've Heard Many Times That Maintaining Tire Pressures Is Very Important. Maintaining your tire pressures is one, if not the most important maintenance task you perform. This is particularly so on a motorcycle.