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Simple answer right here and now - it's like Steve says. It may have been in the old days front tires in our size weren't available so a rear had to suffice. Too bad that wasn't explained in the manual. It has to do with tire construction and the expected load on the tire. If it's a rear tire being used on the rear, point the arrow in the direction of rotation. If that rear tire is used in front (it can be done if necessary), where braking is the load not driving force, the tire needs to be reversed. I'd definitely go with the tire markings if there was any question.
"...he proceeds to insist that my front tire is on backwards."Was the tire positioned so the arrow was on the bottom? If so, it would have pointed backwards.
Point them in the direction you want to go, you already know where you've been.