Like McDave, I also shoot lefty to maintain a more balanced back muscle development. But I actually started after slightly injuring my right hand, which prevented me from drawing, but not from holding/gripping the bow while drawing lefty.
At first, it felt very awkward. I missed terribly, and I also had to close my right eye since it's my dominant one. The learning curve was actually very fun, though, and now I can shoot better lefty than righty for some reason. I also noticed that my target panic went completely away. I could hold at anchor without having that urge you release prematurely, at least when I first started. But now that I've gotten so used to it, I have to consciously maintain more control at anchor like I do when shooting righty.
Either way, I find it a lot of fun being able to shoot both ways.