All that's been said above is good stuff, but here's another angle on the matter--my son is RH and very left eye dominant. Once I figured that out, I started "gently" suggesting that he start shooting LH, thinking that I was doing him a big favor in the long run. At the time, he already had a RH bow that he really liked. Furthermore, since he had already been shooting for a while, doing everything RH was comfortable to him.
My gentle but consistent hints about LH shooting didn't resonate with him, and he really hasn't shot his bow much at all since then.
In hindsight, I should have left it alone and let him decide for himself (although I still would have pointed out to him that it might be easier for him LH, but let it go after that). Although my intentions were good, from the point of view of a youngster I took the fun out of it for him--he didn't embrace the change and it took the fun out of it for him.
Although I wouldn't consider myself to be too "over the top" on these kinds of things, I still managed to forget that it should be fun first and foremost.