Picking up Leads

When  a horse picks up a lead, most people think that the horse will pick up the "correct" lead, but what is the "correct" lead? What if I want a counter canter, then the "wrong" lead becomes the "correct" lead.  Another questoin arises about when the rider puts his/her leg back, the horse should move it's hindquarters over, but how does a person teach a horse that?  Most novice riders have no idea that behind the cinch means move the hips over, and thus they don't teach their horses to move it's butt around.  By teaching the horse to move it's hips, thus helps teach the horse to pick up the correct lead. The horse needs the lope/canter to start witht the hips and then the front end comes.  But which way do the hips need to go?  The right lead would require the rider to put his/her left leg back and thus asking the horse's hips to move to the right.  This would be opposite for the left lead.  The opposite leg should be open (or away from the horse) or can be up by the shoulder, to help push the shoulder in the opposite direction.  This takes a lot of practice and time of working on moving the hips and picking up the lead.  It won't be an overnight success. Horses that are more athletic will tend to pick up the "correct" lead easier, but most horses are right or left leaded, meaning they prefer one or the other.  Most horses are left leaded or tend to like things to the left, mostly because most of what we as humans do with the horse is mostly all from the left.  WE need to change it up, work from the right.  But I've also had horses that were right leaded as they picked up the right lead all the time.  Sometimes this is due to body build and conformation.  Other times this is caused by training errors, injuries, or lack of knowledge.  If you need help, please seek the help of a professonal.