Not only did horses and their care stop being 'necessary for society' in certain areas of the world, horses also became militarily unnecessary.
Because automatic weapons, barbed wire, landmines, chemical weapons, and more accurate artillery were invented. Precursors already existed, but the advances made into military technology before and during WWI outmoded the use of cavalry for pretty much everything.
Limited military use cases for horses still remain, but in the past horses pretty much held the roles we give to tanks, APCs, trucks and light vehicles today. Or, the versions of those roles that existed without access to other technologies that enable modern logistics like refrigeration, real-time communication, timekeeping if you go back far enough.
Horses didn't go away overnight, and had been in decline for a while by the late 1800s. When firearms became portable and accurate enough to be wielded as the primary military weapon, a firing line could potentially shred cavalry. Then automatic weaponry allowed only a few operators to do that. By the 1910s it was pretty much over.
The reason I am saying all of this is that today, all of the tack, clothing, equipment, and practices attributed to the most widespread (read: post-colonial) equestrian styles are former military technology. I do not just mean 'english style' riding, 'western style' riding also is: just with more steps in between, from the cavalry use during the Spanish Reconquista (they kept the moorish influences, though!) that informed later use of horses by Conquistadors in Mexico, who brought cattle to Mexico, which necessitated cattle workers also learning equestrian skills, etc. Today, western-style riding has also been adopted by certain modern militaries as well, for the use cases that still call for horses. So there is no dodging the militarism there.
This is why horses used to be a 'boy thing' in many parts of the world. Today, horses being a 'girl thing' means that a lot of the equipment those girls & women are stereotyped using are deadass just formerly military equipment. When the use of short-range munitions becomes outmoded I suspect it will become a 'girl thing' to go to your bunker and lovingly fondle your collection of lockheed hellfire missiles.