Here are some reasons:
You should turn a rear tire around to run it on the front, to run against its direction arrows. This is because of the way the tread joint is made on the tire. When braking, the forces generated will try to open the tread jointing of a rear tire on the front. This will be prevented if the tire is run in reverse direction
The tread is applied to a tire as a flat wide strip of rubber. When molded, the pattern is added. The ends of the tread sections obviously have to be joined together prior to molding. The ends of the tread are not butt jointed together, but cut at a steep angle & then joined together. This obviously makes the joint area larger to help absorb the stress placed upon it. Therefore because they are joined at an angle, if you rotate the tire in one direction you will (in effect) close the joint once every rotation. If you rotate it in the other direction you will try to open the joint once every rotation. The rear tire rotation direction arrow is noted to close the joint on every rotation of the tire as it is put under power.
The same tire would have to be mounted against its rotation direction arrow on the front because although in normal use the joint is running the wrong way. There is no force being applied to it (the front wheel is just running along without the application of power). When you brake, a strong force is pushing from the rear to the front of the motorcycle and this would open up the tread joint, possibly leading to the tread shearing. If you run the rear tire backwards on the front, braking forces will then be trying to close the tread joint, which is overall the best situation.
Tis a little complicated, I know, but I hope this helps a little.