When
Rebuilding Bottom Brackets, use a set-up similar to this which will help to ensure that the wrench does not slip off of the narrow nut faces. The lean on it and watch for movement. I use a good condition 12" or 15" adjustable wrench for this task...
Do not try to move the cup much. Just get it moving and don't worry about stripping the thread with minimal movement. If it moves one way, stop and then try the other. You should feel a difference in the torque required to move the nut. Go with the movement that feels the easiest, probably right hand as others have suggested.
Hope this is a help and I loved my
Gianni Motta Personal, even though it was a touch too large for me...
Hope this is a help.