Teaching the Sidepass Without Rushing the Hindquarters
The common fault is not that the horse cannot do it. It is that the hind end is being asked for more than the front, so the horse drifts across crooked and learns that as the answer.
A sidepass is the horse moving sideways with the front and back travelling at the same rate, staying straight through the body. It looks simple and it is one of the most commonly taught badly, because it is usually taught as one movement rather than two.
The two halves
The horse has a front end and a hind end that can be moved independently, and a sidepass is both of them moving across together, in step.
Almost every problem people run into comes from teaching it as a single request. The horse gets asked to go sideways, offers whichever end is easier to move, and receives a release for it. Repeat that a few times and you have taught the horse that sideways means swinging the quarters over while the shoulders stay put.
That is not a horse that has failed to learn a sidepass. It is a horse that has correctly learned the thing that was actually rewarded.
Teach the ends separately first
Get the hindquarters yielding reliably from a light signal on both sides. The horse should step the inside hind across in front of the outside hind, without rushing and without swinging away.
Then get the forehand yielding, which most horses find harder and most people practise less. The shoulders step across while the hind end stays broadly where it is.
Both of these want to be genuinely established before anything is combined. If either one is sticky, the combination will default to whichever is easier, which is how the crooked version gets built.
Whichever end the horse finds easier will take over, unless the other end has been schooled to the same standard.
Then combine, slowly and in small amounts
Ask for one step across with both ends, and stop. Reward that, and build from there.
The reason for going a step at a time is that straightness is easy to keep for one step and hard to keep for five. Building on one correct step produces a straight sidepass. Asking for a lot of steps and correcting the drift produces a horse that is being corrected constantly and does not know what the target is.
If the hind end starts to lead, stop asking for sideways and go back to the forehand yield until it is level again. If the front leads, work the hindquarters.
The two common faults
Rushing is the first. Sideways is a lateral movement and it wants a rhythm rather than a scramble. A horse that is hurrying is usually a horse that is uncomfortable with the question, and slowing the request down solves more than repeating it faster ever does.
Bracing through the neck and jaw is the second. A horse that goes sideways with a locked neck is bracing against the ask rather than moving away from it, and that generally traces back to too much pressure or too late a release.
From the ground and from the saddle
Establishing it in hand first is worth the time, because you can see what both ends are doing, which you cannot do from the saddle.
The translation to ridden work then goes better, because the horse already knows the movement and is only learning a new set of signals for something it can already perform. Teaching the movement and the aids simultaneously asks the horse to solve two problems at once, and it is the slower route despite feeling faster.