The surface dried before it was used
CommonRolled fondant stays pliable because glucose or glycerine holds water in it. Exposed to the air it loses that water at the surface first, and a skin forms within minutes. The skin is the same material with less water in it and much less give, so the moment it is stretched — over a corner, around a shoulder, off a rolling pin — it splits while the fondant beneath it is still perfectly workable. Every dusting of icing sugar on the bench does a smaller version of the same thing, taking dry sugar into the surface and moving it further from the ratio that made it pliable.
What to change
Keep it covered, and stop dusting it with icing sugar
Knead, roll and lift in one go, and wrap anything that has to wait. Dust with a little cornflour or roll on a non-stick mat rather than working icing sugar into the surface. If a skin has already formed, knead it back in with a very small amount of white vegetable fat rather than with water, which will make it sticky rather than pliable.
Rolled fondant and sugarpaste that cracks as it is applied or shows dry, feathered edges. Not a fix for cracking that appears hours later on a finished cake, which is the cake moving underneath.
Trade-off: Working faster leaves less time to get the covering positioned, which is its own source of tearing.