How old is your baby ?
I experienced the same thing in the first few weeks after baby's birth. He seemed to have trouble latching on the left side and no problem on the right. No idea why, but as he grew and got the hang of breastfeeding it was ok and the side didn't make a difference.
Strange thing with me is, my oldest child used to prefer the left but my new baby prefers the right. I used to think it was to do with how I was most comfortable or which breast produced most milk, but now I think it's more to do with the baby's preference!
although my baby doesn't have a preference but maybe it's to do with which side they feel more comfortable lying on. if i don't use a pillow/ cushion for support, there definetely is a difference depending which arm bears most of the weight in holding her. she feels more comfortable and settles quicker when she is lying on my left arm more.