It's got nothing to do with hand capability, you've misunderstood. For an ambidextrous person, using right-handed scissors in their right hand will work properly, using right-handed scissors in their left hand will work poorly. And vice versa for left-handed scissors.
When holding scissors, the bottom blade is held fairly steady. The top blade tends to get pushed away from the rest of the hand by the action of the thumb. If the top blade is on the far side of the scissors (away from the hand), the far blade edge will get pushed towards the near blade edge when the thumb handle is pushed away (because the blade is on the other side of the hinge from the handle). If the top blade is on the near side of the scissors (the hand side), by pushing the thumb handle away from you, you are separating the two blades rather than pushing them together.
So on right handed scissors, with the thumb handle facing up, the thumb blade is on the left side of the hinge. That way the natural "push away" force from the thumb will keep the blades close together when held in the right hand. On left handed scissors, the thumb blade is on the right side of the hinge, for the correct push-together force when held in the left hand.