What is this aviation quote?
This quote is from Barry Schiff, a retired pilot from TWA and aviation consultant (but this is only the beginning of the story, I invite everybody to read the article on Wikipedia):


Photo stolen from AOPA



Your recollection is accurate! This is indeed in One Six Right.


Landing on 16R at Van Nuys, Youtube

He says that at the beginning (3:06) of the documentary. The video is not available online, but the first sentence of this quote is often taken up, e.g. on page 39 of this Midwest Flyer issue.

The quote in its context:


  “Asking someone why they love to fly is almost like asking someone why
  they like Picasso. The beauty is the fact that you can’t really
  describe it, it’s something that you have to behold. Flying takes you
  into another dimension, literally. We see, feel, and experience things
  that people who don’t fly will never know.”
  
  Barry Schiff, Aviation Safety Expert / Pilot (source)