My experience might be completely irrelevant to you, but I'm going to share it anyway.
My horse is quite a well educated horse. Done lots of dressage and eventing. So he is pretty good at flexing around corners.
I got on him and he COULD NOT for the life of him flex to the left. I thought it was him, because I had never seen him ridden by someone else. I actually, for a while, thought I'd been duped, because he was nothing like I was told he was. He COULD NOT flex left, he NEVER picked up the left canter lead, he would not load on a trailer (still struggles with that, but I figured out why and we're getting through it), he bolted, he bucked...
IT WAS ALL ME. I sorted ME out, and suddenly my horse was sorted. Flexing around every corner and curve, no more bolting, no more bucking. Canter leads perfect nearly every time. We're now doing counter canter, flexed to the inside (very difficult for the horse), to the outside (what they naturally want to do in counter canter), all beautifully balanced. Trot at all different speeds from a western pleasure jog right up to a HUGE lengthened trot that covers more ground than the average horse's canter.
I sorted myself, and suddenly I had a completely different horse.
So, your horse might actually know, and you might not know how to ask for the flexion. Lessons are brilliant ;) I had two dressage lessons, not even on my horse, and I've been riding so much better since then and it's REALLY showing in how Monty works.