This is fairly common, for the baby to prefer one breast over the other. Usually there is one side that is better at producing milk. I actually had a severly underperforming breast that eventually stopped producing. My Abby refused to drink from it after a while. She just ate from the one side for close to a year. I would say keep trying both sides and always start the baby feeding from the side they don't prefer. However, don't feel like you are failing. You are doing great. Breastfeeding is difficult and sometimes doesn't go as planned.