Could be your breasts are similar to mine. My RHS is pretty useless, LOL! The flow is slower and the capacity is less. Both kids have preferred my LHS from the get-go and both my girls have completely given up on the RHS by about 8-9mo. The only time I can get Phoebe to take my RHS is in the middle of the night, and even then she won't feed for long.
If its any consolation, it is possible to only feed from one side (though not ideal of course, but possible). I often look quite lopsided, but feeding time is less stressful now that we just don't bother with the right.