Our adoption of right-handed threads as the norm comes, I'm guessing, from two
things: our natural tendency to right-handedness and the mechanics of the
lathe.

By itself, our right-handedness should have no great effect in determining
thread direction. But it did determine that lathes - from the earliest
woodworking lathes onward - were built with the headstock on the left. I've
never seen one with the headstock on the right, but wouldn't rule it out. The
mechanics of the lathe dictate that the work generally turn toward the user.
So we're now locked into a machine in which the work or the tool, looking
toward the headstock, turns counter clockwise.

It all follows logically from that point. Spindle threads? Well, they've got
to be right hand or they'll loosen with use. Wooden threads? At one point,
they were all chased by hand. No difference between right and left, right?
Not quite. It's just as easy to chase a LH thread as a RH one on a lathe,
provided it's external. Chasing an internal thread is a different matter. RH
gets the nod. Taps and dies in the lathe? Again, the CCW rotation favors RH
over LH.

There are a few non-lathe processes that seem to favor RH threads over LH.
Twist drills or augers in a bit brace, for example. (Except maybe for the
left-handed person). With screwdrivers there may be a small edge. By and
large, though, I'm betting that it was the lathe that sewed things up in favor
of the RH threads.

John Martin