The horse's tail is connected to its spine. And because of that, it really tells the story of the state of the horse's back. While attempting to judge the true carriage of the horse by looking at his head and neck can be deceptive and difficult to discern, the tail does not lie.
A good halt is square because it was a good halt. Not because the rider has taught it the "trick" of squaring up after an unbalanced halt.
If your horse finds lateral exercises more difficult in one direction vs the other (as many do), then they are not truly straight, or evenly laterally supple.
"I used to ride mostly Thoroughbreds. I don’t know if they’re more intelligent, but I find that they think for themselves a bit more than the warmbloods. With a warmblood I find I definitely have to do a lot more, and think a lot more for them.
In the sport of Eventing, ensuring that our horses are truly fit for our level of competition is one of the best ways to prevent unnecessary injuries.