This subject has come up heaps of times and the answer is usually that the non dominant hand gives a better shave as you are more cautious with it.
I imagine that as your confidence and technique improve the added caution would diminish though.
for what its worth I have been at this for 3 years now about.
I used to shave with my right hand only and my shaves on the left side of my face used to suffer. Now I use my left hand and it has improved my shaves considerably on that side of my face but it still wont quite match my right side.
Its probably a combination of things but our faces are not actually perfectly symmetrical. I feel my left side is slightly more hollow with a more pronounced cheek bone. I have to compensate by inflating the cheek slightly. I don't need to do this on the right side for some reason.
When I was first starting out I noticed that I was indeed doing better with my non-dominant hand. I am now happy to say that I have corrected that problem and get the same shave on both sides :)
LOL - was thinking this the other day, only I took a different approach, can one side of the blade be sharper than the other?
Still to this day, I think it's technique, but if I'm rushed, or not quite in the Zen mode, or I'm using a blade I haven't used in awhile, I'll get the slight stubble on my neck on the left side, which means my dominant hand isn't doing as good a job as my left hand (non-dominant)...but yes, I sometimes get an inconsistent shave, and what's funny is sometimes it's with razors that gave a BBS shave a week or two before...for me, I think it's mood, the position of the stars...but yes, it happens.
I think you might be nuts, but no worries, you're in the right place.
I get a better shave on my right side. While it happens to be my dominant side, I don't believe that's the reason. I just can't get ATG on my left side as close. It's not the angle of the stroked..just weird whiskers on that side..