Baby prefers one side?

I've just noticed this pattern through the night last night. My son woke up the first time and I fed him on the right side. I have always only offered one side at each feeding and it's always worked. As he ate from the right side he kept squirming and unlatching and eventually turned his head away after about 13 minutes of nursing, wide awake. I tried for the next half hour to get him to sleep (it was 2 am lol) and he just wouldn't. Finally I decided to try feeding again and he nursed from my left side for 30 minutes, not squirming or unlatching and fell asleep. Thought it was a weird fluke but he just woke up again, squirmed and unlatched the entire time he nursed on my right side, gave up after about 10 minutes, and now he's nursing happily from my left side. I can hear him swallowing when he eats from my right side so I know he's getting milk, though I do leak more from my left side throughout the day. Any ideas?