Very often horses are much more willing to bend toward their soft or concave side. They are already "bent" on that side and they naturally
take outside rein better, they feel softer on inside rein and easier to sit on that side. One of the main reasons for it is position of their back as it curves gently around rider's inside leg
it also drops down a touch on inside to allow the rider to have a "place" to sit into. This happens due to a specific characteristic of the mammal spine including human's one.
The vertebras on the side where spine is naturally concaved to are also rotated slightly down as a consequence the other side is convex and also pushed up.
Bending on concave side
When a horse is bending on the concave side the rider feels that his/her inside seatbone has a place to sit right into the horse with inside leg dropped down more vertically
than outside leg, the inside leg also have an easy time staying near the girth because horse's body "creates" a place for it. Outside leg has more "horse" under it and wraps around the horse to stay behind the girth. This creates a clear feel for the rider that he/she sits more on inside seatbone. The challenge of bending concave side is in not allowing more bend than necessary and also being very aware of balance in the reins. If a horse starts to feel strong on inside rein it is because he is falling out through his outside shoulder and uses inside rein as a support to fall from.
Bending on convex side
When a horse tries to bend on convex side it is hard for him to create a bend through the spine which requires stretching muscles on opposite concave side, engaging muscles on long convex side and slightly rotating vertebras downward on convex side which are not used to such action. A rider must be aware of such tendencies and clearly feel horse's evasions to be able to change them. Otherwise, the horse will push the rider's inside seatbone up rendering it useless, most likely even push it to outside placing rider's inside seatbone in the middle of his back and dropping outside seatbone down. The rider has a false feeling of having more weight on inside seatbone. But the problem is rider's seatbones are not level, and not in the center being left and right of horse's spine. The inside leg in such situation starts to slide backwards: first, in attempt to regain a sense of balance that rider's body knows it has lost; second, because horse's ribs are bulging to the inside and the
rider's inside leg has no "place". The leg sits "on top of a hill" and slides off either forward or backward at first chance. It is impossible to fix this situation properly without addressing the horse's back and the ribcage. Simply working inside rein alone will not do it. If rider kicks with his/her inside leg when it is in a wrong place and/or when the rider is sitting in the wrong place the action simply displaces the haunches instead of creating bend. I have seen cases where horses push up so much on convex side that I had to focus all my attention on not letting them push my seat up and out. Every time I succeeded at the task bending was easy to accomplish.
When bending the convex side it is important not to push too much down with the upper thigh of outside leg as this will encourage the horse to displace his ribcage to his favorite position diminishing or eliminating the bend. A rider must feel that he/she sits more toward the inside of the horse with outside leg rather softly wrapped around outside part of horse's barrel without too much gripping or pushing down.
If you click here
you will open one of my pictures where I am riding Santo to the left. This is a moment during 10 m circle in trot. I am trotting toward the camera. You can clearly see that my inside leg appears more vertically down compare to outside leg which has more bend in the joints. Santo's ribcage is flatter on inside, he has gentle curve to the left in his whole body. Santo is fairly balanced as the line drawn down from between his ears following the line of his face will continue through the middle of his body parallel to his right front leg that is in a stance phase. My upper body on the other hand is not so well balanced :) If I draw a line through the two buttons of my coat it will not match Santo's line. This is because I am leaning forward more than I should :)
Also, if you subscribe to Dressage Today
there is an article on passage by Hubertus Schmidt in June issue of 2013. Two pictures where horse is moving toward the camera show opposite trot phases. In both pictures it is clear that the whole horse is positioned to the left. Rider's inside leg is more vertical, she is sitting more into her inside seatbone and it looks like the horse gives her the room to sit there.
Position and actions of rider's seatbones play a major role in how well a horse will bend. Very often riders lose the bend in circles, shoulder-ins, half-passes, etc because they do not recognize that their seatbones have lost their position, not centered, not level and the horse is pushing them up or making them slide down without rider's awareness of the problem. Reins and legs can do only so much in this situation. Working on the seat, developing quiet, well placed seatbones is of outmost importance to become an effective rider.