That would have to be one super-germ to spread so fast before burning out.-A plague drives humanity extinct
-A plague drives horses extinct
If that is true, then how come horses weren`t domesticated in those parts of Europe where they roamed and where agriculture was practiced from at least 6000 BCE on? It appears that the domestication of horses there was a cultural import from the East arriving at least 3,5000 years later.These are basically the only plausible PODs to prevent horse riding. Agriculture was likely inevitable, agriculture begets domestication, horses are prime domesticates. Even if we contend that domestication happens off the steppe, at some point someone will have the idea to ride the things, and at some point someone will take them out on the steppe and realize they're basically unstoppable.
Also, OTL`s domestication spread well into societies which weren`t agricultural at all, once the developed package had emerged - like into Mongolia, where horses abounded, yet previous herding societies had not domesticated the Przewalski horse for a couple of millennia, either.
As an explanation, I would argue that in many contexts, horses aren`t really prime domesticates. There are much better meat providers around in most areas of the world: cattle, sheep, goats, pigs - unless you`re living in a cold steppe where horses can feed themselves by accessing grass by digging through crusted snow surfaces which cattle doesn`t do. There are better (stronger, sturdier, more enduring, more mountain-adaptive) beasts of burden: oxen, donkeys, onagers. There are much better (quantity-wise at least) milk / dairy providers around (at least cattle; maybe even sheep and goats?). As for leather, I`m no expert. Horses are not really low-maintenance animals, either. Either way, the big advantage of horses throughout later history was their supreme military capacities: they`re very fast, faster than any of the other animals mentioned. But THAT advantage only came to fruition once the necessary inventions had been made to use them for pulling war wagons, and when the war wagon had become outdated, horses kept their advantage because by that time they had been transformed through breeding into animals which could be ridden fast and far by strong grown-up men.
The neolithic agriculturalists of, say, SOuthern France, when they saw a horse, I think they saw an animal they considered rather untameable and not worth that effort, rather one fit for being hunted. The same attitude prevailed with regards to WILD horses into modernity when they became extinct - only by then you had, of course, tame competitors.
Horses were only prime domesticates under rather specific circumstances - some of which required previous domestication effects, so for primary domestication, it´s even less.