None of my nieces or nephews ever purred. But, I could see where
  cats are like children, just not the inverse.

  Lower form to higher form.

  Unless of course you have human as lower form and cat as higher,
  which is also perfectly fine. Not everybody follows the same
  Taxonomy.
  But that is my bias: I have the same remark with "the brain is
  like a computer" and I consider it a mistake (I don't know the
  name of the mistake) to go from higher to lower. But it's far
  more common to say "the brain is like a computer" rather than
  saying, "the computer is like a brain". Seems like nitpicking
  but saying/teaching it wrong for decades _has_ led to some weird
  ideas about a superiority of computers over humans. Faster? Yes.
  Superior? No.