I think any riding teaches any rider to control their emotions. Any emotion has consequences in performance and horses clearly amplify this effect: one of the life lessons that riding teaches. I noticed during one Olympics that so many of the athletes were shown on the podium with tears flowing - except in the equestrian disciplines where athletes remained dry eyed.
I recall an article in Horse & Hound many years ago which asked the question “How to encourage boys to ride?” O.K. it was half jokey but, in my memory, never ask them to do anything that is difficult, boring or dirty, make certain they can win any competition they enter and, ideally, have a few other boys to socialize with at shows and at home in the stables. It does make one think. Foxhunting, Polo, Skill at Arms, Triathlon tend to hold the interest of boys rather than dressage.
At university we set up a “Learn to Ride Programme” for people who had never before sat on a horse and participants paid up front for a block of lessons. Unexpectedly, it was invariably men who signed up - a cunning plan: they would meet women if they learnt to ride! However, a group of college-age men learning together proved to be very successful because they supported each other, had fun and there was little ego involved as each was as bad as the other. I think about half who started riding carried on which is a good stat for people trying a new sport.