First thing, check your tack. Does everything fit correctly? Then make sure when you sit your horse that you aren't holding the reins tightly as this could cause a miscommunication, especially with a curb. Try this exercise some time, when there are no other horses. Completely DROP your reins, just let them hang down and give a nice even squeeze with both legs like you are squeezing a giant tube of toothpaste and your horses mouth is the hole the paste would come out of. Does it move forward with the reins dropped? If yes, then you are holding your reins too tight.
But if no, then it sounds like you may have a buddy sour horse on your hands that will not go without a friend. This isn't fun and will take a LOT of work and patience to get through. You will need to work without the presence of other horses as often as you can and NOT let your horse get away with this. I'm not sure what level rider you are, but it sounds like you may need a trainers help with this one. Someone who can help you make the immediate corrections your horse needs exactly when it needs it to get it to stop this stubborness. If it were my horse, I would give it a good smack with a popper or crop and MAKE it go forward, even if it's just a walk at first. You need to assert that YOU are the boss, not the horse.