This is an entry into the 16th Fortnightly Challenge : reverse-puzzling
Person 1: Look at the paper.
Person 2: Yes, I see, I see, but I don't know what cipher this is.
Person 1: Okay, let me give you a hint: The outset of airplane becomes the edge of airspace.
Person 2: What does that even mean?
Person 1: And the opposite.
Person 2: What opposite?
Person 1: The outset of backyard is outset.
Person 2: What?
Person 1: And the opposite.
Person 2: Seriously, what does that mean?
Person 1: The outset of car is the edge of plane.
Person 2: I have no idea what this means.
Person 1: Remember, and the opposite is true, too!
Person 2: Okay, only now did I get it. I know what cipher this is.
Sadly, you do not have the previously mentioned paper. Can you find what cipher this is?