Maybe try a egg but snaffle and loosen up your reins
Try using a little less bit. Snaffle will work wonders along with some flexing. Reward positive behavior
bump the right rein and hold the left out towards you right knee and bump harder the right and softer on the left do this until he does what's you want, horses learn on release not ptessur
Mine did the same. I use waterford bit and try to be ad light on the hand as I can. For me, fighting him or pulling up didn't work.
If he's not listening to your use your other aids. For example, if he starts to lean on the reins squeeze with your leg and push him up and into the contact don't just pull up!! You can also lean back a little and push your body weight back and in slightly and leg to push him forwards and out!!😊:)
Maybe he has A wound in his mouth On the right side. Otherwis you should try and put A lilltle bit more leg when you try putting him more on your left rein.
He's probably just being stubborn. Smack him lightly with a crop when he does this to tell him he can't get away with it any more