I'll tell you what I was taught, but I don't follow it so take it with a few pounds of salt...
Imagine the horse's feet form a rectangle. At a sitting trot, use the outside leg to shove his hip over, so the rectangle is now moving across the ground with his inner front leg a little ahead of the outer one. If he sidepasses, move the outer leg further back until his HIP moves. From that position, squeeze both legs to accelerate to a canter, with the inside front leg ahead of the outside front leg.
When prepping to learn to canter, Trooper & I practiced this a lot. But when I eventually asked him to canter, he always took a left lead. That is a flexibility & training issue for him, and we've worked on it for the sake of his physical ability.
However, I'm mostly in the category of not caring what lead the horse chooses. Outside the arena, my turns at a canter would either be very gradual, or unpredictable. Either way, setting a particular lead wouldn't help me much.
On a lesson horse, I'd make sure with my instructor that I'm asking him properly. In my limited experience with lesson horses, some seem inclined to do the wrong thing deliberately so that the instructor will stop them to 'correct the student' while they get to relax.
If I was your instructor - and you probably ought to thank God that I am not! - I'd say, "Goody! He wants to teach you the counter-canter! It is more work for him, and you'll be rougher on his back, but if that is what he wants..." Then I'd let you learn to ride a rough canter, and let the horse learn that he doesn't get a break by doing things wrong.