Here is a copy of a post by WGTniv explaining why there is no left handed avatars.
Hey everybody,
We do hear you lefties on this matter, but there is a technical hurdle we must overcome in order to be able to do it. Unfortunately, it's not a simple matter of reversing the Avatar because there are other parts of the avatar that you may not have noticed before.
For example, if knock your drive into some brush on Bethpage you may notice some "extra" grass around your feet. That's called a stencil. We use the stencil to make your avatar look like he's standing in the grass rather than on top of it. The stencils we have created are designed to interact with the ground surface from the perspective of a right handed player, so the extra "grass" is displayed (appropriately) at their feet.
Each and every hole is thoroughly mapped so that the right stencil is used in the right places. The trouble with mirroring really becomes visible in cases where the avatar would be standing in the fairway (on the far right side) and the ball is in the rough. Those lies/stencils are all mapped specifically for right-handers so that (in this case) no stencil is drawn at your feet because your avatar is standing in the fairway. The exact opposite occurs on the left side of the fairway where your avatar may be standing in brush instead, but the ball lies in the fairway. Even though the ball is in the fairway, the avatar is standing in deep grass and a stencil is used where the avatar itself is standing. In this case, if the avatar was left handed and in the right hand rough you'd see him standing in the rough, but the rough stencil would be basically be growing out of the fairway (where a righty would normally stand). Obviously that's not appropriate nor desired. =)
Along with creating left handed avatars we will need to remap the stencils for lefties on every hole to avoid those odd situations I described above. On top of all of this we will still need to rework the avatar animations, the club animations (all clubs are drawn right handed at the moment) and we also must consider whether or not we would need to completely reverse the GUI itself to provide a right-to-left meter/interface instead of a left-to-right meter/interface.
We do plan to implement this feature eventually, but this should help you guys gain a little understanding about the process and see that there's a little bit more than meets the eye here.