Anarchy means without leaders [0]. There are many types of anarchism that have a flat hierarchic structure and could still be considered organizations.

What parent was suggesting is closer to nihilism, which is a common misunderstanding because in films anarchism is generally portrayed as nihilism[1].

  [0]https://en.wikipedia.org/wiki/Anarchy#Etymology
  [1]https://en.wikipedia.org/wiki/Nihilism