Was he doing this before, is this new? if so, it could be a growth spurt. Even now, after months of nursing from one side per session, there are days when Kate wants both. You can try using compression on the first side to help him get milk out more easily. I tend to have an oversupply so Kate got used to a fast flow.... and when she mostly drains one side she gets really mad that the flow is so slow.

Is it only on your left side? What about when you start on your right? Do you nurse more often on your right? Most people do have one side that produces more than the other... it's not necessarily an issue. (For me it was because I favor laying on my left side in bed, so she nursed more from the left than the right at night.) It's not necessarily a problem.