Why is my horse refusing to turn left?

Basically when I try to turn Rio left he won't turn unless I really pull him to the left. He isn't doing this so much when I want him to go right, it's just left. And when I do pull him he stops first every time like he thinks i'm pulling back on the reins and telling him to stop. I ride western and I am currently using a tomb thumb snaffle on him. Also, I always try to have a light hand with him but since he's been doing this when I do he won't turn. The problem could be me but I'm not sure. So why could he be doing this?