Hi, I'm new on this forum and just having a bit of a ramble around. Noticed your recent post and scanned the replies and thought I could be of some help.
Cantering off on the wrong leg is probably one of the most common problems so everybody will have experienced that at one time or another. So take heart, I will try and explain simply what is going on and how to correct it.
Ignoring for a moment what you may or may not be doing, novice horses always want to "fall in" at the shoulder. A simple way to see this is to walk alongside the horse in the school, with the horse on the outside. As you start to walk a corner of the school the shoulder of the horse will get closer to you and you may be forced to step in of the track to avoid the horse walking all over you. This will likely be worse on one rein compared to the other. Worth remembering which is the better rein.
So now for what the rider needs to do ............ I will make the assumption that your basic riding position is not too bad, bacause that will obviously have an affect and becomes a whole new discussion.
First practice some leg yield on both reins, both in walk and then rising trot. Points to note here are to keep the body of the horse fairly straight (commonly riders flex the neck to the inside too much) and make sure the outside leg is "off" (commonly riders use the inside leg to ask the horse to step over but this becomes blocked by the outside leg also being "on"). This is where you should start to feel the inside leg getting the horse to work into the outside rein, make sure you don't through that extra bit of contact away and keep the hands together.
Now we are ready to practice canter transitions. So starting on the better rein we remembered earlier, rising trot down the long side of the arena. At the quarter marker initiate the turn with the outside rein and ask for a step of leg yield into the corner. If you do this correctly and hold the contact in the outside rein the horse will become more rounded in the neck. Sit and outside leg back to ask for the canter strikeoff and all being well will be correct. Suggest half way along the short side of the arena you perform at least one 20m circle so that you and the horse can settle into a balanced rhymic canter.
If the horse has been going off wrong for a long time it may take a few attempts for the horse to get it right. Same applies for you to get the step of leg yield in the corner and the timing of the leg aids.
There are a lot of other things that can go wrong, common rider faults like tipping forward or leaning in on the turn etc but I hope I have made some sense and kept things as simple as possible for you
