Way back when, almost all spinning reels were right handed, with the handle on the left. All casting reels had the handles on the right.
My father, being left handed, special ordered left handed Mitchells, with the handle on the right. Nowadays, its been long forgotten that it was this way
When I went from casting reels to spinning reels, I had trouble with learning to reel in with my left hand, so I used one of my dad's old lefty Mitchells. Eventually, I got sick of casting with my right hand and switching, so I forced my self to use a left side handled (a righty model) reel.
For obvious reasons, you cannot design a casting reel that is convertible, like a spinning reel, and that is why I think this comes up. I think its just easiest to refer to a reel as a right or left hand retrieve. I know many right handed people that prefer to use a left handed reel. I use both, and there advantages to certain types of casts, to using one or the other.
I really like I lefty reel for pitching and flipping, especially both of my Daiwa flipping reels, since I can reengage the spool without turning the handle. I also like them for frog fishing, since my stronger arm (right) is pulling the fish out of the pads and slop. Since I palm the reel, and almost always use two hands to cast, a righty suits me better for all other casting situations. My right hand just moves from the reel (or scratching my head, LOL) to the trigger and thumbar, just behind my left. If I need real power, I can move my left down to the butt of the rod.
It may all sound counter intuitive, or wasteful actions, but years of doing make it something I don't think about anymore. I even once had an argument with a fishing buddy about whether I use two hands for casting, LOL. I lost that one - didn't even realize it until I thought about it.
At any rate, repetition of either retrieve will train your muscles and you'll be able to do whatever you want. Some guys can do everything with both hands and both lefty and right reels.