I would say either don't use the rug or get a bigger one. If it's tight enough that you think it's to tight it most likely is. Your horse should have room to move! :)
First of all can you tell me a bit more about why you put a rug? Is it necessary? How is he during grooming? Is he trying to bite also when you try to brush him on the breast? Maybe he just doesn't like it and tries to make you understand.
But i would mostly think that this is because it makes him hurt (especially if you say this is too tight).
Horses don't bite for nothing, thy are trying to give us a message of bad memories, a discomfort or a hurt.
I think you should try to change it, find a bigger one or even put it off.
You should also make him see an osteopath just in case, to have his advice on how he reacts.
I hope i could help you :)