My 14 yr old son is right handed and I started him with a right hand bow before I knew to check for eye dominance.He is left eye dominant. He shotthe right hand bowwell, but soon decided on his own to switch to shooting left hand. He is a lot more comfortable shooting that way. In fact he has trouble shooting right handed now.

It would be better if he learns both ways, but if you have to choose one, go with the eye dominance.