There’s a point in the life of a free-stone peach where it is just ripe enough that the skin will pull off easily in one piece.
You quarter the peach first and pull out the pit. You grab an end of the skin between your thumb and your paring knife. You gently and smoothly pull off the skin.
If you wait too long and the peach becomes a little too ripe, the skin becomes fragile. It gets so delicate that no matter the amount of care you use, it is impossible to pull it off in one piece.
And so, the time-saving nature of the free-stone peach as compared to the cling peach is lost.
Timing is everything.