Well, let's analogize:
  our abilities in nanotech are supreme, and we get all the
  industrial processes right to manufacture everything in the
  proper way to produce a clone.

  Now:
  Across the street, two cars are manufactured and come out
  looking identical.

  The two humans are identical as long as they do nothing.
  The two cars are identical as long as they do nothing.

  As soon as the car leaves the parking lot, it has a distinct
  identity. Hit by different pebbles on the road, forming its
  uniqueness.

  As soon as the clone has its first thought, it's already getting
  hit by different pebbles in the road (sensory data) dinging its
  brain and causing it to respond uniquely.