Twisting them up real quick around your iPod does, in fact, damage the wires. Same thing with old video game controllers that had wires, especially the playstation ones. The way I keep mine from getting damaged and wrap it up real quick is instead of spinning the wires around the iPod, I let the earbuds dangle while I roll the iPod over and over in my hand, reeling in the earbuds. When the earbuds are all rolled up, i tuck the leftover ends inside the loop created where the earbuds plug into the iPod.
It’s quick and it keeps the earbuds right on the iPod instead of dangling and the wires don’t get twist damage. Just don’t wrap them too tight!