I don't know why we have decided that your main hand (?!?!) is the one you strum and pick with. Think about it: you're doing something that's very complicated in both hands, so whichever hand you pick for what side of the guitar doesn't really matter.
I met an Italian guitar player once (performed with all kinds of world famous people) who was right handed and played left handed guitar.
I asked him about it, and he said that he just didn't know how he was "supposed" to do it, when he first taught himself. And that was the way that came naturally to him.
So don't worry, you're not weird!
Anders