NH - I know and have worked with one righty who hews mirror image opposite of the way I do. There's as many ways as there is skinless cats.
For me it just makes sense, I work to the right of everything, no matter what tool I am using, so the workpiece is convenient to my dominant hand. I can't fathom why anyone would do otherwise.
I have one Axe hung the opposite way, what I would call righty and you would call lefty. A Goosewing, paid more for it and use it less than any other ax. I use it when contrary grain demands I hew backwards.
Interestingly, as mentioned recently in another thread, I bought my only Gränsfors used from another lefty, when she bought it she ordered what the catalog described as a left handed Ax, she opened the box to find a wrong handed ax. They were good about exchanging it for what they see as right handed, and she and I see as left handed.
Gabel - Post away, unless my landing pad is too shiny or too much of my belly is falling over my belt.
"We build too many walls and not enough bridges" - Isaac Newton