I'm 11 and left handed but I play guitar right handed. Kurt Cobain of Nirvana played simulary; he was right handed, but he played left handed. If the strumming is easier than fretting, then shouldn't you do the fretting with your dominant hand? So why do you have to play the difficult way?
You know, I've wondered about that myself a number of times, but I've still never come up with a decent answer. Maybe it isn't as hard to coordinate your left fingers as it is to coordinate other muscles in your left hand? For example, when you type on a keyboard, it isn't any easier to type with your right hand than with your left hand.
That's just a bunch of speculation, but I hope it helps!