After I got into uni late 1950s I was given a ride as a reward. We hacked in a group, straight out onto Epsom downs - me on a lead rein and we cantered. It didnt feel frightening at all. In those days one learned canter in forward seat. It seemed very easy.
I was on a hack in France and I'd done a length of the arena but not much and the RI would call out the instructions in French and the person in front translated what it was to me in English and he called it out and the person in front said "canter" and we cantered half away around a field, walked the diagonal route back to the start and did again another three times!! I was having the time of my life!!! We were on a flat price of grass and the RI said something in French and the person in front just turned around and said "gallop" and off we went!! I haven't tried gallop since but luckily I knew how and managed to stay on!! It was a miracle but yeah thats how I learnt!!
Lots of people fret that they havent learned to canter sooner. But I have met others who were put off riding by being allowed or made to canter too soon.
Please take care. Cantering on a horse that will not stop may not be safe for a beginner, especially in a school arena with corners. On the other hand if you are out hacking and cantering beside another horse, that may be a good way to learn.
By the way, many polo ponies are ridden and trained to canter and not trot. But they are trained to have brakes.
Can’t remember how I learnt to canter but I was out with my adult son who does not respond well to formal lessons. We were trotting across Dartmoor. My girl was really trotting out, I turned round and young Moss was cantering. I didn’t say a word, just slowed down and asked son what he thought. I thought that trot was smooth was his response. He just got sitting to it. The only time he had a formal canter lesson he fell Off!