Balancing a broomstick on the hand: „Try it with the broom facing up or facing down. What is easier? Try it with a shorter or a longer broomstick. Try walking with a broomstick balanced on the hand.“
Explanation in general:
To have something completely balanced, the center of gravity must be steady/right above the balancing hand. If the top moves out of the gravity center the movement of the hand has to follow directly in this direction.
Broom facing up:
The center of gravity is higher. This means the speed to react can be lower