It used to be, years ago that tire makers warned never to change rotation direction when rotating the tires. The steel cords supposedly did not like rotating in reverse direction from what they were "used to" and would occasionally come apart and break the cords. I saw this once in the Air Force (1980). A sergeant showed me a truck tire with cords showing out the rubber. And he thought this had happened because of rotating the tire from one side to the other. But he could have been wrong, for all i know.
Now sometimes i have to swap tires side to side on the front just to find a pair that wont make the car pull to the side.
The pulling drives me nuts (which wouldn't be a long drive really

); so i just took the risk. So far, so good.