front tire mounted backward

Come on now, that is all a conspiracy so we will not run car tires on our bikes oser

A tire should turn only in one direction (if it's a dirt bike tire it really doesn't matter) Many people who install a rear tire on the front reverse the direction. That does not make sense. Unless your bike is really weird, both tires turn in the same direction and that is what counts. I have (sadly) a front wheel drive transportation car, and because the front tires do everything, they wear out noticeably faster than the back tires. Every once in a while I switch places with the front and back tires (on the same side of the car) to even out the wear, check the brakes, etc. The point is, front or rear, the tires turn in the same direction. Same thing on a bike. You should not mount a tire backwards, as some of them can start to come apart from rolling the wrong way because of the way the plies are designed. If you put a rear tire on the front, put it on in the same direction as you would if it were going in the back.

Wrong. A tire mounted on the rear of a motorcycle gets stressed in the opposite direction vs a front tire.
The rear is stressed by acceleration, while the front tire stress is predominately from braking.
If you choose to mount a "rear tire" on the front, it should be mounted "backwards".

+1 I've NEVER seen that guy make any sense.

Be aware that a front tire mounted backwards will also make your odometer run backwards. This is not cool. If you're an honest fella, you'll re-mount it correctly.