A bitless bridle is a kind and very copfortable bridle for your horse but it is not good for strong horses. Are you sure he is strong? Is he not just trying to resist the bit? Maybe get him checked up just incase.

my horse use to fight all the time with me when she wore a bit, from pulling to head shaking and walking around with her nose pointing right up in the air and no brakes ,it started to become very un nerving .i had her teeth checked all was fine and tried all sorts of bits (happy mouth ect) so out of desperation i went out and bought  a hackamore  come home and tried it . Wow was like riding a different horse she was light and responsive with perfect breaks even bought her head back out of the clouds and could ride her on a long rein .the best thing ive done for my horse and i ,wether hacking or schooling we are now both happy and relaxed and growing together as a partnership 

 I have 13 horses, all shapes, sizes, ages and breeds, all but one goes absolutely beautifully in Dr. Cook's Bitless Bridle.  The one that still needs a bit is a little horse that I acquired from someone who left out "steering" during training and she found out that she's stronger than us!  A bit is the only way to get through to this mare!  

A bitless Bridle will not make a badly trained horse all of a sudden behave....it will make a trained horse much more comfortable and behave better.