Question

If a cup of water has holes in it than why does no water come out when when it is falling?

Answer 1

Because the acceleration of gravity is the acceleration of gravity.
It doesn't matter what the mass of a falling object is, and it  doesn't
matter whether a falling object is solid or liquid.  ALL falling objects
fall with the same acceleration, reach the same speed, and hit the
ground at the same time.

If there was no air in the way, then a feather, a school bus, and a
battleship would accelerate at the same rate, fall together and hit
the ground at the same time.

When you drop a cup full of water that has holes in it, the cup and
the water fall with the same acceleration, reach the same speed,
and hit the floor at the same time.  Then, THAT's the time to go
and get the mop.
  

Answer 2

On earth, if something isn't being held up it will accelerate downwards due to gravity. So if you hold onto a cup with a hole in it, the water will be pulled downwards through the hole and end up on the floor.