I'm left handed but shoot left.

Left handed people live in a right-handed world. Cars (in North America are right handed), scissors are right handed, can openers are right handed, computers are right handed, most musical instruments are right-handed. The list goes on and on.

That said I think left handed people SHOULD have an advantage hitting left. My theory with "handedness" is it is dependant on the FIRST time you do something. Once you start doing fine motor skills it get wired into your brain and it's very difficult to unwire.