Andrew is right. The belief is (in the salty fraternity in the USA anyway) that there is barely any difference in the strength of both arms in terms of hanging off the rod playing a big fish so no issues with using the left arm. However, if you are right handed, the theory goes that your right hand and arm will tire less quickly than your left and you will therefore be able to maintain co-ordination for reel winding longer with the dominant right hand, hence right hand wind for a right handed fisherman (counter-intuitive for most), ergo more chance of landing the fish. That's according to some bloke called Lefty Kreh anyway
I fish double handers and single handers for fresh and salt species, and all my reels are set up for left hand wind. It really would be a pain in the a r s e to swap a 15ft spey rod from hand to hand during the fight, because of the long lower handle.