First, review your equitation. Are you sitting balanced and asking for the canter with proper cues? Are your hands, seat, and legs quiet when neeed and active when needed? Have someone video you as you ask for the canter. This may give you the answer to your question.
Second, review your tack. Is your saddle fit correct? What kind of bridle/bit are you using and is it properly adjusted? Any issues with pads, stirrups, spurs, etc?
Third, review your husbandry. Is the horse properly trimmed and, if necessary, shod? Does your farrier trim the horse to anatomical correctness and properly balance the foot? Lots of information on the Web about this. A gaited horse should be trimmed/shod like any other horse.
Fourth, review what you know about the horse's training. It's not uncommon for owners of young Walkers to delay teaching the canter until the horse is "set in gait." Often any attempt to canter will be punished. So the horse might just be fearful of being hurt for doing what you ask.
Fifith, review the horse's conformation. Are there any deficiencies that will inhibit proper cantering?
It is very hightly probable that if you get through this entire list you'll find the issue. If not, then you'll need some "professional help."
When you begin to teach the canter do so on a straight line. Don't attempt any turns. On the straight, ask for the canter as softly as possible. If you get a correct response let the horse go two or three strides then back to the gait or walk (where you began). Profusely reward the horse. Don't worry about trying to "rate" the speed. Then do it again. Then go for the other lead (start, by the way, with easiest lead; most horses will favor one over the other). If you don't get the proper response immediately come back to the walk/gait, rebalance the horse, and try again.
Once you get a good transition increase the number of strides. Don't try any turns for several sessions. The longer the straight, the better off you are. When the Cavalry had a problem teaching the canter the Remount Centers all used a fence, about a half mile long. They would start by practicing transitions and increasing the time in gait. Eventually they would have the horse canter along the fence its entire length, on both leads. THEN they would begin to ask for turns.
For vast majority of horses an inability/difficulty in performing an action will lie with the rider. Most of the time it's found in equitation practices, tack practices, or husbandry practices. The video camera is your friend, here, but also a major "smug basher." It's hard on rider's egos to see that a problem is not the horse's but theirs.
Still, if you want to get past this you might have to "eat some crow" on your practices. From extensive personal experience believe me when I say the there's no way to make "crow" taste good.
Good luck with your project.