I often have to explain this phrase to people who never seem to have heard it before.

My logical explanation goes something like this:
"The difference between x and y is the same as the the difference between y and x."
This has the advantage of making people say "you can't argue with that." and leaving you to say it whenever you want.

What I usually actually mean when I say this is:
"Well, it's a difference, I don't care much about what it actually is. You probably just corrected me and now I'm 1. embarrassed that I missed it, 2. I didn't care enough in the first place to notice."
I would like to say that my reason for using this phrase was mostly the second one, but I'd be lying.