There's so much unknown not being able to see what's going on. At this stage, riding with contact just means that you are always "feeling" your horse's mouth with a steady and light pressure and his mouth is going to move your hands. So when his head moves back and forth at the canter, your hands follow his mouth. This is IMO pretty difficult to learn and not something you master right away. A horse I work with has the most sensitive mouth and absolutely HATES if you are all but extremely soft and steady with your hands and he responds by throwing his head around. I wonder if this is happening to you? Your trainer is right, if you are a western rider you probably think you are too tight on the reins when you aren't, but you may not be steady enough with your hands to be able to ride with that short of a rein without hitting your horse in the mouth or pulling on them. It's a hard distinction. You don't want to *hang* on your horse's mouth, you just want to always *feel* it.
A few tips...
1) Before you can have steady hands you MUST have a rock solid position. A "pretty good" position doesn't cut it. You must be balanced and completely secure with a correct leg. Your leg is what keeps you secure in an english saddle, some people refer to it as your "foundation". So without a foundation how can a house stand? It can't. So without a solid leg, how can your body be balanced? It can't. So you will be unsteady and using your hands on your horse's mouth to balance. Position position position!
2) You can't be tense. When you are tense your arms can't be soft and following. If you are scared your horse will act up, you can't be soft and following. And your horse can feel it! Tension can also make your body to drive a sensitive horse and make them faster or more nervous.
3) While you can't be stiff, you also can't let your hands jiggle or post with your body either (so common!). Your horse feels your every tiny hand/arm movement in his mouth. This drives certain horses crazy. :) Your hands need to be very steady as they follow.
Again, if this horse is making you nervous and unable to teach you how to ride with contact, this horse is probably not the one for you right now!