Yes, my Arab used to clench his jaw and flip his chin in the air when you went to remove the bridle. The bit would then whack him in the teeth and you were lucky if it didn't whack you in the head on the way out too. It took a long time of asking him to put his head down and slowly removing the bit to get him over it. If you can, maybe try unbuckling the cheek piece and taking the bit out that way for a while? That way you can take it out really slowly and can still have a feel of his head with the rest of the bridle while you do it. Some horses really object to the bit clanking on their teeth on the way out so try to avoid it hitting his teeth, and see if that helps.