Your experience with horses is limited.
I've posted before that my family has owned a farm for over 50 years. Hundreds of students learned to ride there, and I'd say just about every one of them posted in their first lesson and cantered within weeks.
Yes, my experience is limited. However, I'm not a fool. Please notice what I wrote - "And when I've visited stables and watched students cantering, a lot more bounced the canter than rode the canter. I also saw folks trying to force their horse to canter while they were still pulling on his mouth, and wondering why he refused.
We had a French exchange student visit us this summer. He had ridden ponies some years earlier, but they were small ponies and he had not ridden in years. He took a turn riding Mia, and he cantered. Yes, he stayed on. Yes, she behaved herself - ears pinned as he bounced and hung on the reins, but she behaved herself. He didn't ride her again.
Yes, I know people often canter within a few rides, as my DIL did. The reason my DIL cantered on her second time on a horse was so she would learn it wasn't scary, and that if her horse cantered later on, to just ride him and not panic. But that did not mean she wasn't hard on his mouth and back while cantering. As I described - she bounced the canter
. There is a big difference between staying on at a canter, and "someone attempting and [succeeding at] a full following seat and [not] punishing the horse's back in the process.
Now consider the OP's situation: "...I have been doing it regularly for about 2-2 1/2 months now but just started riding Cinder
". And it seems Cinder is less than thrilled to canter or gallop. Could there be a link? Hmmm....
Without seeing her ride, I don't know. Staying on a canter is easy. Riding a full following seat and doing it well is not something I've seen many do within a couple of rides. And when it is not done well, some horses avoid it.
It's that very bounce that may be causing her to refuse to pickup the canter/lope. Something you do work on in lessons is smoothly sitting the trot.
...That being said, if the horse isn't comfortable with the way you're riding, she may not canter. It's that simple. And if there's nothing wrong with saddle fit or the horse physically, it's entirely possible you need more riding experience and skill to be on this horse...
Post 39 (mine):
...And when I've visited stables and watched students cantering, a lot more bounced the canter than rode the canter. I also saw folks trying to force their horse to canter while they were still pulling on his mouth, and wondering why he refused...Thinking about when I was learning to ride, and watching my family members learn to ride - none of us had any business cantering before 9-12 months of riding...
Hmmm...I guess I'm missing what I wrote that is so radical. "...there are only two criteria of your position; a) are you in fluid balance and rhythm with your horse or not? B) does your seat enable you to control your horse efficiently?
" - V.S. Littauer
Maybe my idea of what constitutes being "in fluid balance and rhythm with your horse" differs from others. And if you are not comfortable sitting the trot, then I think cantering should be for fear-avoidance only. Also - I've seen a lot of new riders posting the trot in a way that would make me pull them off of my horse. Doing it gently and fluidly seems to be harder than what the folks I've seen in southern Arizona normally achieve on their first lesson riding...