Can someone explain why all four tires must be replaced on a Subaru if only one is damaged?

It's not actually the tranny that takes the bulk of stress bit the differentials. To simplify it, take a stick with a wheel on either end. If they are the exact same circumference wheels, the stick will roll perfectly strait. But if there is even a slight difference in the sizes of the rollers, the stick will automatically turn. So to combat this, there is a differential in the middle which is a small clutch pack that allows either side to turn at a different speed over uneven surfaces or hard turns. Problem is if you are cruising down the freeway at 55 with slightly different sized tires left to right, that differential will burn up trying to keep both sides turning the same speed. It's really just the price of driving an AWD car.

As long as the tires, as manufactured, are the same outside (rolling) diameter or very close (usually within about 3%), you DO NOT NEED to replace all four. However, you should always, in ANY car, replace tires in twos -- the front axle set or the rear axle set. EXCEPTION: You've bought new tires within a couple of hundred miles and one blows out. You can replace the single blown tire.

And you're basically right about the designed "slop" for uneven pavement, tire slip, etc. Today's Stability Management systems, however, will note significantly different rotations per distance traveled and try to compensate for what they interpret as tire slip. The sensitivity of these systems varies.

NOTES: Some cars actually have different wheel diameters front to rear; the Management systems have been calibrated to account for that. While mixing tire brands / tread designs front and rear is possible if the rolling diameters are compatible, it's not recommended. Never mix different tires on the same axle.

they usually are only reqd to be sold in pairs. say your rear passenger tire went flat. If they only put one brand new tire there and leave the original one on the rear driver, the tractions are different. brand new vs worn. so one tire will be working harder to grip the road than the other leading to un even distribution of workload and other problems. i usually replace all 4 when one goes out though cause they always have a better deal for all 4

you dont have too, but it is a better idea because the one tire will have better traction than the others, then the diff will try to give more power to the 3 wheels instead of 4 and you want equal power.

sounds like someone is trying to rip you off

get more money out of the buyer

You don't need to.