Up going up and down going down makes sense. I don't understand why you would invert them.
I played flight sims with joysticks for years before the anologue stick became ubiquitous. So in my mind, the right abalogue stick worked like a joystick; i.e. pull back on it to look up, push it forward to look down.
I guess you could think of the anologue stick as representing a person's head. You move your head forward to look down, back to look up.
I've tried on occasion to leave the controls as they are in FPS games, but I just can't play properly with the Y axis being inverted. I guess it's just what you're used to.
Obviously, I don't invert the X axis and I don't invert the Y axis when using a mouse.