Very good point, Tim. Switching hands can alter the angle, direction just enough to completely change the cutting ability.
Personal example: On my neck, going from under my chin to my adam's apple; When I shave the right side of that area with a downward pass using my right hand....total WTG. I could go over that area over and over using that hand and I'll reach a threshold where it additional passes just don't make for a smoother shave. With the simple act of switching to my left hand and shaving the EXACT same right side below chin downward to adam's apple is a total ATG feeling. I get closer in one left hand pass this way that I can at all with a ton of right hand passes.
Chris L
Have you ever tried shaving only with your left hand with the grain on the left side of your face and against the grain on the right side?